dorsal/arxiv
View SchemaA Poincar\'e-Birkhoff-Witt theorem for generalized color Lie algebras
| Authors | Cesar Bautista |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706016 |
| URL | https://arxiv.org/abs/q-alg/9706016 |
| DOI | 10.1063/1.532471 |
| Journal | J. Math. Phys. 39 (1998) 3828-3843 |
Abstract
A proof of Poincar\'e-Birkhoff-Witt theorem is given for a class of generalized Lie algebras closely related to the Gurevich S-Lie algebras. As concrete examples, we construct the positive (negative) parts of the quantized universal enveloping algebras of type A_n and M_{p,q,e}(n,K), which is a non-standard quantum deformation of GL(n). In particular, we get, for both algebras, a unified proof of the Poincar\'e-Birkhoff-Witt theorem and we show that they are genuine universal enveloping algebras of certain generalized Lie algebras.
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"abstract": "A proof of Poincar\\\u0027e-Birkhoff-Witt theorem is given for a class of\ngeneralized Lie algebras closely related to the Gurevich S-Lie algebras. As\nconcrete examples, we construct the positive (negative) parts of the quantized\nuniversal enveloping algebras of type A_n and M_{p,q,e}(n,K), which is a\nnon-standard quantum deformation of GL(n). In particular, we get, for both\nalgebras, a unified proof of the Poincar\\\u0027e-Birkhoff-Witt theorem and we show\nthat they are genuine universal enveloping algebras of certain generalized Lie\nalgebras.",
"arxiv_id": "q-alg/9706016",
"authors": [
"Cesar Bautista"
],
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"q-alg",
"math.QA"
],
"doi": "10.1063/1.532471",
"journal_ref": "J. Math. Phys. 39 (1998) 3828-3843",
"title": "A Poincar\\\u0027e-Birkhoff-Witt theorem for generalized color Lie algebras",
"url": "https://arxiv.org/abs/q-alg/9706016"
},
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