13 citations · 46 across the 16 of their papers we have counts for
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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…
Lie polynomials in an algebra defined by a linearly twisted commutation relation
Rafael Reno S. Cantuba
We present an elementary approach in characterizing Lie polynomials in the generators of an algebra with a defining relation that is in the form of a deformed or twisted comm…
A Casimir element inexpressible as a Lie polynomial
Rafael Reno S. Cantuba
Let be a scalar that is not a root of unity. We show that any polynomial in the Casimir element of the Fairlie-Odesskii algebra cannot be expressed in t…
Lie polynomials in -deformed Heisenberg algebras
Rafael Reno S. Cantuba
Let be a field, and let . The -deformed Heisenberg algebra is the unital associative -algebra with generators and…
A Lie algebra related to the universal Askey-Wilson algebra
Rafael Reno S. Cantuba
Let denote an algebraically closed field. Denote the three-element set by , and let denote the free unital…