Computer Science – Symbolic Computation
Scientific paper
2011-08-04
Proceedings of CASC 2011, by Vladimir Gerdt, Wolfram Koepf, Ernst W. Mayr, and Evgenii Vorozhtsov (eds.), Lecture Notes in Com
Computer Science
Symbolic Computation
13 pages, 5 tables
Scientific paper
We consider algebras over a field K, generated by two variables x and y subject to the single relation yx = qxy + ax + by + c for q in K^* and a, b, c in K. We prove, that among such algebras there are precisely five isomorphism classes. The representatives of these classes, which are ubiquitous operator algebras, are called model algebras. We derive explicit multiplication formulas for y^m*x^n in terms of standard monomials x^i*y^j for many algebras of the considered type. Such formulas are used in establishing formulas of binomial type and in implementing non-commutative multiplication in a computer algebra system. By using the formulas we also study centers and ring-theoretic properties of the non-commutative model algebras.
Koutschan Christoph
Levandovskyy Viktor
Motsak Oleksandr
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