Algebras Generated by Finite Subgroups of Unitary Groups
Group representation theory is one of the most powerful tools to study groups. The unitary group is an important research branch of group theories. We study a class of algebraic structures generated by unitary groups，and we prove that Alg( H) is a von Neumann algebra for any subgroup H of the unitar...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | zho |
| Published: |
Harbin University of Science and Technology Publications
2021-04-01
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| Series: | Journal of Harbin University of Science and Technology |
| Subjects: | |
| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1952 |
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| Summary: | Group representation theory is one of the most powerful tools to study groups. The unitary group is an important research branch of group theories. We study a class of algebraic structures generated by unitary groups，and we prove that Alg( H) is a von Neumann algebra for any subgroup H of the unitary group U( d) . Then we show that group algebra ［G］，generated by a finite group G，is isomorphic to a direct sum of some von Neumann algebras of Type Ⅰn for distinct values of n. We further discuss what kinds of von Neumann algebra of Type Ⅰ can be generated by a finite unitary subgroup. It is of great significance to study the algebraic structure of the generation of subgroups of unitary groups for the establishment of Schur-Weyl duality of unitary groups and permutation groups. |
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| ISSN: | 1007-2683 |