Contractions on ranks and quaternion types in clifford algebras
In this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element. Each contraction is a sum of several summands with different basis elements of Clifford algebra. We consider even and...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2015-03-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20435/16682 |
| _version_ | 1811330260400078848 |
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| author | Dmitry S Shirokov |
| author_facet | Dmitry S Shirokov |
| author_sort | Dmitry S Shirokov |
| collection | DOAJ |
| description | In this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element. Each contraction is a sum of several summands with different basis elements of Clifford algebra. We consider even and odd contractions, contractions on ranks and contractions on quaternion types. We present relation between these contractions and projection operations onto fixed subspaces of Clifford algebras - even and odd subspaces, subspaces of fixed ranks and subspaces of fixed quaternion types. Using method of contractions we present solutions of system of commutator equations in Clifford algebras. The cases of commutator and anticommutator are the most important. These results can be used in the study of different field theory equations, for example, Yang-Mills equations, primitive field equation and others. |
| first_indexed | 2024-04-13T15:58:39Z |
| format | Article |
| id | doaj.art-565a1ee2d6e64413adc86eb7354c8d7a |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:58:39Z |
| publishDate | 2015-03-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-565a1ee2d6e64413adc86eb7354c8d7a2022-12-22T02:40:36ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812015-03-0119111713510.14498/vsgtu138717855Contractions on ranks and quaternion types in clifford algebrasDmitry S Shirokov0A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of SciencesIn this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element. Each contraction is a sum of several summands with different basis elements of Clifford algebra. We consider even and odd contractions, contractions on ranks and contractions on quaternion types. We present relation between these contractions and projection operations onto fixed subspaces of Clifford algebras - even and odd subspaces, subspaces of fixed ranks and subspaces of fixed quaternion types. Using method of contractions we present solutions of system of commutator equations in Clifford algebras. The cases of commutator and anticommutator are the most important. These results can be used in the study of different field theory equations, for example, Yang-Mills equations, primitive field equation and others.https://journals.eco-vector.com/1991-8615/article/viewFile/20435/16682clifford algebrascontractionsprojection operationsquaternion type |
| spellingShingle | Dmitry S Shirokov Contractions on ranks and quaternion types in clifford algebras Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki clifford algebras contractions projection operations quaternion type |
| title | Contractions on ranks and quaternion types in clifford algebras |
| title_full | Contractions on ranks and quaternion types in clifford algebras |
| title_fullStr | Contractions on ranks and quaternion types in clifford algebras |
| title_full_unstemmed | Contractions on ranks and quaternion types in clifford algebras |
| title_short | Contractions on ranks and quaternion types in clifford algebras |
| title_sort | contractions on ranks and quaternion types in clifford algebras |
| topic | clifford algebras contractions projection operations quaternion type |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20435/16682 |
| work_keys_str_mv | AT dmitrysshirokov contractionsonranksandquaterniontypesincliffordalgebras |