Direct limits of graded matrix algebras
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866909983264735232 |
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| author | Kochetov, Mikhail Yasumura, Felipe |
| author_facet | Kochetov, Mikhail Yasumura, Felipe |
| contents | The direct limit of finite-dimensional semisimple associative algebras arises as a purely algebraic counterpart to important $C^\ast$-algebras. In this paper, we classify direct limits of matrix algebras endowed with a grading by a finite abelian group over an algebraically closed field. In particular, we give an explicit description of the graded $K_0$ group of the direct limit of matrix algebras, and we provide conditions under which this limit absorbs graded-division algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03503 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Direct limits of graded matrix algebras Kochetov, Mikhail Yasumura, Felipe Rings and Algebras The direct limit of finite-dimensional semisimple associative algebras arises as a purely algebraic counterpart to important $C^\ast$-algebras. In this paper, we classify direct limits of matrix algebras endowed with a grading by a finite abelian group over an algebraically closed field. In particular, we give an explicit description of the graded $K_0$ group of the direct limit of matrix algebras, and we provide conditions under which this limit absorbs graded-division algebras. |
| title | Direct limits of graded matrix algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2601.03503 |