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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…
Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras
E. R. Filimoshina, D. S. Shirokov
This paper introduces and studies generalized degenerate Clifford and Lipschitz groups in geometric (Clifford) algebras. These Lie groups preserve the direct sums of the subspaces…
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…
A Note on Centralizers and Twisted Centralizers in Clifford Algebras
E. R. Filimoshina, D. S. Shirokov
This paper investigates centralizers and twisted centralizers in degenerate and non-degenerate Clifford (geometric) algebras. We provide an explicit form of the centralizers and tw…
Noncommutative Vieta Theorem in Clifford Geometric Algebras
D. S. Shirokov
In this paper, we discuss a generalization of Vieta theorem (Vieta's formulas) to the case of Clifford geometric algebras. We compare the generalized Vieta's formulas with the ordi…