Classification of elements of clifford algebras according to quaternionic types

Shirokov, D. S.

doi:10.1134/s1064562409040401

Cited by 15 publications

(20 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the operation of anticommutator. The notion of quaternion type was introduced by the author in the brief report [48] and the paper [56]. Further development of this concept is given in [52], [57], [61], [66], see also books [35], [55].…”

Section: Quaternion Types Of Clifford Algebra Elementsmentioning

confidence: 99%

Clifford Algebras and Their Applications to Lie Groups and Spinors

Shirokov

2018

GIQ

View full text Add to dashboard Cite

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, Dirac equation in different formalisms, spinors in n dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the method of averaging in Clifford algebras, the notion of quaternion type of Clifford algebra elements, the classification of Lie subalgebras of specific type in Clifford algebra, etc. MSC : 15A66, 22E60, 35Q41

show abstract

Section: Quaternion Types Of Clifford Algebra Elementsmentioning

confidence: 99%

Clifford Algebras and Their Applications to Lie Groups and Spinors

Shirokov

2018

GIQ

View full text Add to dashboard Cite

show abstract

“…Let us consider Cℓ p,q as a vector space and represent it in the form of the direct sum of four subspaces of quaternion types 0, 1, 2 and 3 (see [1], [2], [3]):…”

Section: Lie Algebras Of Specific Type In Clifford Algebras and Lie Gmentioning

confidence: 99%

Classification of Lie algebras of specific type in complexified Clifford algebras

Shirokov

2017

Linear and Multilinear Algebra

Self Cite

View full text Add to dashboard Cite

We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical matrix Lie algebras in the cases of arbitrary dimension and signature. We present sixteen Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups.

show abstract

“…Let us consider the Clifford algebra Cℓ R (p, q) as the vector space and represent it in the form of the direct sum of four subspaces of quaternion types 0, 1, 2 and 3 (see [6], [7], [8]):…”

Section: Clifford Algebras and Quaternion Typesmentioning

confidence: 99%

“…If p−q ≡ 1 mod 4. Then matrices (8) are block-diagonal and we have the following matrix representation of Cℓ R (p + 1, q + 1). For p + q generators we have the same and for the last two generators we have…”

Section: Matrix Representations Of Real Clifford Algebras In Some Casesmentioning

confidence: 99%