Mixed tensor invariants of Lie color algebra
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909303442505728 |
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| author | Pattanayak, Santosha Samuel, Preena |
| author_facet | Pattanayak, Santosha Samuel, Preena |
| contents | In this paper, we consider the mixed tensor space of a $G$-graded vector space where $G$ is a finite abelian group. We obtain a spanning set of invariants of the associated symmetric algebra under the action of a color analogue of the general linear group which we refer to as the general linear color group. As a consequence, we obtain a generating set for the polynomial invariants, under the simultaneous action of the general linear color group, on color analogues of several copies of matrices. We show that in this special case, this is the set of trace monomials, which coincides with the set of generators obtained by Berele. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixed tensor invariants of Lie color algebra Pattanayak, Santosha Samuel, Preena Representation Theory 17B10, 17B35, 17B65, 14M30 In this paper, we consider the mixed tensor space of a $G$-graded vector space where $G$ is a finite abelian group. We obtain a spanning set of invariants of the associated symmetric algebra under the action of a color analogue of the general linear group which we refer to as the general linear color group. As a consequence, we obtain a generating set for the polynomial invariants, under the simultaneous action of the general linear color group, on color analogues of several copies of matrices. We show that in this special case, this is the set of trace monomials, which coincides with the set of generators obtained by Berele. |
| title | Mixed tensor invariants of Lie color algebra |
| topic | Representation Theory 17B10, 17B35, 17B65, 14M30 |
| url | https://arxiv.org/abs/2409.02068 |