Twisted Traces and Positive Forms on Generalized -Weyl Algebras
Let be a generalized -Weyl algebra, it is generated by , , , ⁻¹ with relations ⁻¹ = ², ⁻¹ = ⁻², = (⁻¹), = (), where is a Laurent polynomial. A Hermitian form (⋅,⋅) on is called invariant if (, ) = (, ⁻¹), (, ) = (, ), (, ) = (, ⁻¹) for some s ∈ C with || = 1 and all , ∈ . In this paper, we cl...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211536 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Twisted Traces and Positive Forms on Generalized -Weyl Algebras. Daniil Klyuev. SIGMA 18 (2022), 009, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730606593441792 |
|---|---|
| author | Klyuev, Daniil |
| author_facet | Klyuev, Daniil |
| citation_txt | Twisted Traces and Positive Forms on Generalized -Weyl Algebras. Daniil Klyuev. SIGMA 18 (2022), 009, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let be a generalized -Weyl algebra, it is generated by , , , ⁻¹ with relations ⁻¹ = ², ⁻¹ = ⁻², = (⁻¹), = (), where is a Laurent polynomial. A Hermitian form (⋅,⋅) on is called invariant if (, ) = (, ⁻¹), (, ) = (, ), (, ) = (, ⁻¹) for some s ∈ C with || = 1 and all , ∈ . In this paper, we classify positive definite invariant Hermitian forms on generalized -Weyl algebras.
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| first_indexed | 2026-04-17T15:05:37Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211536 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:05:37Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Klyuev, Daniil 2026-01-05T12:28:55Z 2022 Twisted Traces and Positive Forms on Generalized -Weyl Algebras. Daniil Klyuev. SIGMA 18 (2022), 009, 28 pages 1815-0659 2020 Mathematics Subject Classification: 17B37; 53D55; 81R10 arXiv:2105.12652 https://nasplib.isofts.kiev.ua/handle/123456789/211536 https://doi.org/10.3842/SIGMA.2022.009 Let be a generalized -Weyl algebra, it is generated by , , , ⁻¹ with relations ⁻¹ = ², ⁻¹ = ⁻², = (⁻¹), = (), where is a Laurent polynomial. A Hermitian form (⋅,⋅) on is called invariant if (, ) = (, ⁻¹), (, ) = (, ), (, ) = (, ⁻¹) for some s ∈ C with || = 1 and all , ∈ . In this paper, we classify positive definite invariant Hermitian forms on generalized -Weyl algebras. I am grateful to Pavel Etingof for the formulation of the problem, stimulating discussions, and helpful remarks on the previous versions of this paper. I would like to thank Mykola Dedushenko for explaining the physical meaning of positive traces on generalized -Weyl algebras. I am grateful to the anonymous reviewers for helpful remarks and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twisted Traces and Positive Forms on Generalized -Weyl Algebras Article published earlier |
| spellingShingle | Twisted Traces and Positive Forms on Generalized -Weyl Algebras Klyuev, Daniil |
| title | Twisted Traces and Positive Forms on Generalized -Weyl Algebras |
| title_full | Twisted Traces and Positive Forms on Generalized -Weyl Algebras |
| title_fullStr | Twisted Traces and Positive Forms on Generalized -Weyl Algebras |
| title_full_unstemmed | Twisted Traces and Positive Forms on Generalized -Weyl Algebras |
| title_short | Twisted Traces and Positive Forms on Generalized -Weyl Algebras |
| title_sort | twisted traces and positive forms on generalized -weyl algebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211536 |
| work_keys_str_mv | AT klyuevdaniil twistedtracesandpositiveformsongeneralizedweylalgebras |