About: Nichols algebra

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Nichols algebra Goto Sponge NotDistinct Permalink

An Entity of Type : yago:WikicatQuantumGroups, within Data Space : dbpedia.org associated with source document(s)
QRcode icon

http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FNichols_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 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.

Attributes	Values
rdf:type	yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:Group100031264 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:WikicatHopfAlgebras yago:Science105999797 yago:WikicatQuantumGroups
rdfs:label	Nichols algebra (en)
rdfs:comment	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 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. (en)
foaf:depiction
dcterms:subject	Quantum groups Hopf algebras
Wikipage page ID	32370851 (xsd:integer)
Wikipage revision ID	1075937888 (xsd:integer)
Link from a Wikipage to another Wikipage	Root of unity List of finite-dimensional Nichols algebras Monster group Cuboctahedron Dynkin diagram Quantum groups Eigenvalue Braided Hopf algebra Braided monoidal category Braided vector space Quantum groups Conjugacy class Alternating groups Ideal (ring theory) Cyclic group Centralizer and normalizer Direct sum Pauli exclusion principle Involution (mathematics) Baby monster group Dynkin diagrams Hopf algebras Poincaré–Birkhoff–Witt theorem Group Hopf algebra Group of Lie type Groupoid Schur lemma Matsumoto's theorem (group theory) Root system Tensor algebra Symmetric group Semisimple Lie algebra Fischer group dbr:Supersymmetry_as_a_quantum_group Yetter–Drinfeld category Weyl group P-group Sporadic group Klein four group
sameAs	Nichols algebra Nichols algebra Nichols algebra Nichols algebra
dbp:wikiPageUsesTemplate	dbt:Mono
thumbnail	wiki-commons:Special:FilePath/Dynkin_diagram_A1A1.svg?width=300
has abstract	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 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, strikingly similar to those of semisimple Lie algebras. A comprehensive introduction is found in the lecture of Heckenberger. (en)
prov:wasDerivedFrom	wikipedia-en:Nichols_algebra?oldid=1075937888&ns=0
page length (characters) of wiki page	29628 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Nichols_algebra
is Link from a Wikipage to another Wikipage of	List of finite-dimensional Nichols algebras Braided Hopf algebra Braided vector space Quantum group
is foaf:primaryTopic of	wikipedia-en:Nichols_algebra

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (61 GB total memory, 46 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software