Anzeige
Erschienen in:
2011 | OriginalPaper | Buchkapitel
On Two-Generated Non-commutative Algebras Subject to the Affine Relation
verfasst von : Viktor Levandovskyy, Christoph Koutschan, Oleksandr Motsak
Erschienen in: Computer Algebra in Scientific Computing
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We consider algebras over a field
${\mathbb K}$
, generated by two variables
x
and
y
subject to the single relation
yx
=
q
xy
+
αx
+
βy
+
γ
for
$q\in{\mathbb K}^*$
and
$\alpha, \beta, \gamma \in {\mathbb K}$
. 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 e. g. establishing formulas of binomial type and in an implementation of 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.