Torus actions on free associative algebras, lifting and Białynicki-Birula type theorems
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866916650363650048 |
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| author | Belov-Kanel, Alexei Elishev, Andrey Razavinia, Farrokh Rowen, Louis Yu, Jie-Tai Zhang, Wenchao |
| author_facet | Belov-Kanel, Alexei Elishev, Andrey Razavinia, Farrokh Rowen, Louis Yu, Jie-Tai Zhang, Wenchao |
| contents | We examine the problem of the linearity of an algebraic torus action in the associative setting. We prove the free algebra analog of a classical theorem of BialynickiBirula, which establishes linearity of maximal torus action. Additionally, we formulate and prove linearity theorems for specific classes of regular actions, and provide a framework for constructing non-linearizable actions, analogous to the work of Asanuma. This framework has applications in the study of the Associative Cancellation Conjecture. Furthermore, we show the existence of two non-isomorphic algebras, whose free products with a polynomial ring are isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_01385 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Torus actions on free associative algebras, lifting and Białynicki-Birula type theorems Belov-Kanel, Alexei Elishev, Andrey Razavinia, Farrokh Rowen, Louis Yu, Jie-Tai Zhang, Wenchao Algebraic Geometry Rings and Algebras 16S10, 14R10, 14R20 We examine the problem of the linearity of an algebraic torus action in the associative setting. We prove the free algebra analog of a classical theorem of BialynickiBirula, which establishes linearity of maximal torus action. Additionally, we formulate and prove linearity theorems for specific classes of regular actions, and provide a framework for constructing non-linearizable actions, analogous to the work of Asanuma. This framework has applications in the study of the Associative Cancellation Conjecture. Furthermore, we show the existence of two non-isomorphic algebras, whose free products with a polynomial ring are isomorphic. |
| title | Torus actions on free associative algebras, lifting and Białynicki-Birula type theorems |
| topic | Algebraic Geometry Rings and Algebras 16S10, 14R10, 14R20 |
| url | https://arxiv.org/abs/1901.01385 |