28 citations · 187 across the 16 of their papers we have counts for
16 papers
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 SVD and Polar Decomposition in Real and Complexified Clifford Algebras
D. S. Shirokov
In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real and complexified…
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…
On Some Lie Groups in Degenerate Clifford Geometric Algebras
E. R. Filimoshina, D. S. Shirokov
In this paper, we introduce and study five families of Lie groups in degenerate Clifford geometric algebras. These Lie groups preserve the even and odd subspaces and some other sub…
On generalization of Lipschitz groups and spin groups
E. R. Filimoshina, D. S. Shirokov
This paper presents some new Lie groups preserving fixed subspaces of geometric algebras (or Clifford algebras) under the twisted adjoint representation. We consider the cases of s…
Calculation of elements of spin groups using method of averaging in Clifford's geometric algebra
D. S. Shirokov
We present a method of computing elements of spin groups in the case of arbitrary dimension. This method generalizes Hestenes method for the case of dimension 4. We use the method…
Covariantly constant solutions of the Yang-Mills equations
D. S. Shirokov
We present a new class of covariantly constant solutions of the Yang-Mills equations. These solutions correspond to the solution of the field equation for the spin connection of th…
Clifford algebras and their applications to Lie groups and spinors
D. S. Shirokov
In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups…
Constant solutions of Yang-Mills equations and generalized Proca equations
N. G. Marchuk, D. S. Shirokov
In this paper we present some new equations which we call Yang-Mills-Proca equations (or generalized Proca equations). This system of equations is a generalization of Proca equatio…
On some Lie groups containing spin group in Clifford algebra
D. S. Shirokov
In this paper we consider some Lie groups in complexified Clifford algebras. Using relations between operations of conjugation in Clifford algebras and matrix operations we prove i…
Calculation of elements of spin groups using generalized Pauli's theorem
D. S. Shirokov
We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formali…
Development of the Method of Averaging in Clifford Geometric Algebras
D. S. Shirokov
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of antico…
Development of the method of quaternion typification of Clifford algebra elements
Dmitry Shirokov
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classificatio…
Quaternion typification of Clifford algebra elements
Dmitry Shirokov
We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyz…
A classification of Lie algebras of pseudounitary groups in the techniques of Clifford algebras
Dmitry Shirokov
In this paper we present new formulas, which represent commutators and anticommutators of Clifford algebra elements as sums of elements of different ranks. Using these formulas we…