4 papers
On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras
E. R. Filimoshina, D. S. Shirokov
This paper introduces Lie groups in degenerate geometric (Clifford) algebras that preserve four fundamental subspaces determined by the grade involution and reversion under the adj…
On Commutative Analogues of Clifford Algebras and Their Decompositions
Heerak Sharma, Dmitry Shirokov
We investigate commutative analogues of Clifford algebras -- algebras whose generators square to but commute, instead of anti-commuting as they do in Clifford algebras. We o…
Determinant, Characteristic Polynomial, and Inverse in Commutative Analogues of Clifford Algebras
Heerak Sharma, Dmitry Shirokov
Commutative analogues of Clifford algebras are algebras defined in the same way as Clifford algebras except that their generators commute with each other, in contrast to Clifford a…
On Unitary Groups in Ternary and Generalized Clifford Algebras
D. S. Shirokov
We discuss a generalization of Clifford algebras known as generalized Clifford algebras (in particular, ternary Clifford algebras). In these objects, we have a fixed higher-degree…