A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)
Let Bq be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q ∈ k θ×θ . Let Lq be the Lusztig algebra associated to Bq [AAR]. We present Lq as an extension (as braided Hopf algebras) of Bq by Zq where Zq is isomorphic to the universal enveloping algebra of a Lie algebra...
| Authors: | , , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2017 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/59990 |
| Online Access: | http://hdl.handle.net/11336/59990 |
| Access Level: | Open access |
| Keyword: | Nichols algebras quantum groups https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | Let Bq be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q ∈ k θ×θ . Let Lq be the Lusztig algebra associated to Bq [AAR]. We present Lq as an extension (as braided Hopf algebras) of Bq by Zq where Zq is isomorphic to the universal enveloping algebra of a Lie algebra nq. We compute the Lie algebra nq when θ = 2. |
|---|