Coalgebra measurings, cyclic theory and homologies of matrix algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908831815041024 |
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| author | Banerjee, Abhishek Kour, Surjeet |
| author_facet | Banerjee, Abhishek Kour, Surjeet |
| contents | In this paper, we consider coalgebra measurings and the maps induced by them between Hochschild and cyclic homology of algebras. We show that these induced maps are well behaved with respect to the various structures appearing on Hochschild and cyclic homology, such as the $λ$-decomposition, the product structure, as well as the module structure of Hochschild homology over cyclic homology. Thereafter, we relate the maps between homology theories of algebras induced by a coalgebra measuring to those induced between homologies of matrix algebras. This is done in the following contexts: (a) cyclic homology and the primitive part of Lie algebra homology of the matrix algebra, (b) Hochschild homology and the primitive part of Leibniz homology of the matrix algebra, and (c) Dihedral homology of an involutive algebra and the primitive part of Lie algebra homology of symplectic or skew symmetric matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coalgebra measurings, cyclic theory and homologies of matrix algebras Banerjee, Abhishek Kour, Surjeet Rings and Algebras Category Theory 16T15, 16E40 In this paper, we consider coalgebra measurings and the maps induced by them between Hochschild and cyclic homology of algebras. We show that these induced maps are well behaved with respect to the various structures appearing on Hochschild and cyclic homology, such as the $λ$-decomposition, the product structure, as well as the module structure of Hochschild homology over cyclic homology. Thereafter, we relate the maps between homology theories of algebras induced by a coalgebra measuring to those induced between homologies of matrix algebras. This is done in the following contexts: (a) cyclic homology and the primitive part of Lie algebra homology of the matrix algebra, (b) Hochschild homology and the primitive part of Leibniz homology of the matrix algebra, and (c) Dihedral homology of an involutive algebra and the primitive part of Lie algebra homology of symplectic or skew symmetric matrices. |
| title | Coalgebra measurings, cyclic theory and homologies of matrix algebras |
| topic | Rings and Algebras Category Theory 16T15, 16E40 |
| url | https://arxiv.org/abs/2602.12505 |