List Of Finite-dimensional Nichols Algebras
In mathematics, a Nichols algebra is a Hopf algebra in a braided monoidal category, braided category assigned to an object ''V'' in this category (e.g. a braided vector space). The Nichols algebra is a quotient of the tensor algebra of ''V'' enjoying a certain universal property and is typically infinite-dimensional. Nichols algebras appear naturally in any pointed Hopf algebra and enabled their classification in important cases.Andruskiewitsch, Schneider: ''Pointed Hopf algebras'', New directions in Hopf algebras, 1–68, Math. Sci. Res. Inst. Publ., 43, Cambridge Univ. Press, Cambridge, 2002. The most well known examples for Nichols algebras are the Borel subgroup#Lie algebra, Borel parts U_q(\mathfrak)^+ of the infinite-dimensional quantum groups when ''q'' is no root of unity, and the first examples of finite-dimensional Nichols algebras are the Borel subgroup#Lie algebra, Borel parts u_q(\mathfrak)^+ of the Frobenius–Lusztig kernel (''small quantum group'') when ''q'' is a ro ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra
In algebra, the Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by \mathfrak(V) and named after the mathematician Warren Nichols. It takes the role of quantum Borel part of a pointed Hopf algebra such as a quantum groups and their well known finite-dimensional truncations. Nichols algebras can immediately be used to write down new such quantum groups by using the Radford biproduct. The classification of all such Nichols algebras and even all associated quantum groups (see Application) has been progressing rapidly, although still much is open: The case of an abelian group was solved in 2005, but otherwise this phenomenon seems to be very rare, with a handful examples known and powerful negation criteria established (see below). See also this List of finite-dimensional Nichols algebras. The finite-dimensional theory is greatly governed by a theory of root systems and Dynkin diagrams, strikingl ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Monster Group
In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order 2463205976112133171923293141475971 = 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 ≈ 8. The finite simple groups have been completely classified. Every such group belongs to one of 18 countably infinite families, or is one of 26 sporadic groups that do not follow such a systematic pattern. The monster group contains 20 sporadic groups (including itself) as subquotients. Robert Griess, who proved the existence of the monster in 1982, has called those 20 groups the ''happy family'', and the remaining six exceptions ''pariahs''. It is difficult to give a good constructive definition of the monster because of its complexity. Martin Gardner wrote a popular account of the monster group in his June 1980 Mathematical Games column in ''Scientific ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra T
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra G4
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra HV3
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra HV2
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra HV1
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra Over Aff7
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra Over Aff5
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra Over A4
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra Over D4
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
|
Nichols Algebra Over S5
Nichols may refer to: People *Nichols (surname) *Nichol, a surname Places Canada * Nichols Islands, Nunavut United States * Nichols, California, an unincorporated community * Nichols Canyon, Los Angeles, California * Nichols, Connecticut * Nichols Farms Historic District, a village within Trumbull, Connecticut. * Nichols, Iowa * Nichols (village), New York * Nichols (town), New York * Nichols, South Carolina, a town * Nichols, Wisconsin, a village * Nichols Shore Acres, Wisconsin, an unincorporated community Military * Nichols Field, a former U.S. air base in the Philippines * Nichols' Regiment of Militia, a U.S. Revolutionary War unit * Camp Nichols, a historic fortification in Cimarron County, Oklahoma Organisations Education * Nichols College, in Dudley, Massachusetts * Nichols School, in Buffalo, New York * Nichols Hall, Kansas State University * Nichols House (Baltimore, Maryland), home of the president of Johns Hopkins University * Nichols Arboretum, Ann Arbor campu ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |