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9 papers · 1 filter
Lie polynomials in a -deformed universal enveloping algebra of a low-dimensional Lie algebra
Rafael Reno S. Cantuba, Mark Anthony C. Merciales
The nonabelian two-dimensional Lie algebra over a field has a presentation by generators , and relation , with the universal enveloping alg…
Lie structure of the Heisenberg-Weyl algebra
Rafael Reno S. Cantuba
As an associative algebra, the Heisenberg-Weyl algebra is generated by two elements , subject to the relation . As a Lie algebra, however, where the u…
Extended commutator algebra for the -oscillator and a related Askey-Wilson algebra
Rafael Reno S. Cantuba
Let be a nonzero complex number that is not a root of unity. In the -oscillator with commutation relation , it is known that the smallest commutator algebr…
Ubiquitous Lie polynomials in a two-generator universal enveloping algebra
Rafael Reno S. Cantuba
The universal enveloping algebra of a two-dimensional nonabelian Lie algebra is a Lie algebra itself with the commutator as Lie bracket. There exists a presentati…
Torsion-type -deformed Heisenberg algebra and its Lie polynomials
Rafael Reno S. Cantuba, Sergei Silvestrov
Given a scalar parameter , the -deformed Heisenberg algebra is the unital associative algebra with two generators that satisfy the -deformed commuta…
An extension of a -deformed Heisenberg algebra and its Lie polynomials
Rafael Reno S. Cantuba, Mark Anthony C. Merciales
Let be a field, and fix a . The -deformed Heisenberg algebra is the unital associative algebra over with generators $A…