Lie polynomials in a q-deformed universal enveloping algebra of a low-dimensional Lie algebra

2025/02/22 by Rafael Reno S. Cantuba, Cantuba, Rafael Reno S., Mark Anthony C. Merciales +1
Mathematics · #math.RA

paper · pdf · doi:10.48550/arxiv.2502.16074

Abstract

The nonabelian two-dimensional Lie algebra over a field \mathbbF has a presentation by generators A, B and relation [ A,B]=A, with the universal enveloping algebra having a presentation by generators A, B and relation AB-BA=A. A well-known fact is that the said Lie algebra is isomorphic to that which has a universal enveloping algebra that has a presentation by generators A, B and relation AB-BA=B. Given q,r,s∈\mathbbF, solutions to the Lie polynomial characterization problems in the corresponding q-deformed universal enveloping algebras, with generalized relations AB-qBA=rA and AB-qBA=sB, respectively, are presented.

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