arXiv subjects

Cesar Bautista

Publications and source records attributed to Cesar Bautista.

3 recordsLinked to original sources

arXiv1998

Quantum Lie algebras of type A_n positive, PBW bases and the Yang-Baxter equation

We show explicitly a generalised Lie algebra embedded in the positive and negative parts of the Drinfeld-Jimbo quantum groups of type A_n. Such a generalised Lie algebra satisfy axioms closely related to the ones found by S.L. Woronowicz. For the universal enveloping algebra of such generalised Lie algebras we establish several conditions in order to obtain bases of type Poincaré-Birkhoff-Witt. Besides a graded algebra is proposed and some relations with the quantum Yang-Baxter equation are studied.

math.QA↗

arXiv1998

The positive part of the quantized universal enveloping algebra of type A_n as a braided quantum group

A generalized Hopf algebra structure for the positive (negative) part of the Drinfeld-Jimbo quantum group of type A_n is established without make any use of the usual deformation of the abelian part of sl_{n+1}.

math.QA↗

arXiv1998

A Poincaré-Birkhoff-Witt theorem for generalized color Lie algebras

A proof of Poincaré-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 Poincaré-Birkhoff-Witt theorem and we show that they are genuine universal enveloping algebras of certain generalized Lie algebras.

q-alg↗