Volodymyr Lyubashenko, Anthony Sudbery
Abstract
It is shown that the quantized enveloping algebra of sl(n) contains a generalized Lie algebra, defined by means of axioms similar to Woronowicz’s. This gives rise to Lie algebra-like generators and relations for the locally finite part of the quantized enveloping algebra, and suggests a canonical Poincaré–Birkhoff–Witt basis.
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It is shown that the quantized enveloping algebra of sl(n) contains a generalized Lie algebra, defined by means of axioms similar to Woronowicz’s. This gives rise to Lie algebra-like generators and relations for the locally finite part of the quantized enveloping algebra, and suggests a canonical Poincaré–Birkhoff–Witt basis.
Key concepts: Lie conformal algebra, Mathematics, Graded Lie algebra, Universal enveloping algebra, Algebra over a field, Affine Lie algebra, Killing form, Pure mathematics