On universal Lie nilpotent associative algebras
We study the quotient Qi(A) of a free algebra A by the ideal Mi (A) generated by the i th commutator of any elements. In particular, we completely describe such quotient for i=4 (for i 3 this was done previously by Feigin and Shoikhet). We also study properties of the ideals Mi(A), e.g. when Mi(A...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier B.V.
2015
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| Online Access: | http://hdl.handle.net/1721.1/96327 https://orcid.org/0000-0002-0710-1416 |
| _version_ | 1826205232171843584 |
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| author | Etingof, Pavel I. Kim, John Ma, Xiaoguang |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I. Kim, John Ma, Xiaoguang |
| author_sort | Etingof, Pavel I. |
| collection | MIT |
| description | We study the quotient Qi(A) of a free algebra A by the ideal Mi (A) generated by the i th commutator of any elements. In particular, we completely describe such quotient for i=4 (for i 3 this was done previously by Feigin and Shoikhet). We also study properties of the ideals Mi(A), e.g. when Mi(A)Mj(A) is contained in M[subscript i+j-1](A) (by result of Gupta and Levin, it is always contained in M[subscript i+j-2](A)). |
| first_indexed | 2024-09-23T13:09:27Z |
| format | Article |
| id | mit-1721.1/96327 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:09:27Z |
| publishDate | 2015 |
| publisher | Elsevier B.V. |
| record_format | dspace |
| spelling | mit-1721.1/963272022-10-01T13:23:23Z On universal Lie nilpotent associative algebras Etingof, Pavel I. Kim, John Ma, Xiaoguang Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I. Kim, John Ma, Xiaoguang We study the quotient Qi(A) of a free algebra A by the ideal Mi (A) generated by the i th commutator of any elements. In particular, we completely describe such quotient for i=4 (for i 3 this was done previously by Feigin and Shoikhet). We also study properties of the ideals Mi(A), e.g. when Mi(A)Mj(A) is contained in M[subscript i+j-1](A) (by result of Gupta and Levin, it is always contained in M[subscript i+j-2](A)). National Science Foundation (U.S.) (NSF grant DMS-0504847) 2015-04-02T16:03:58Z 2015-04-02T16:03:58Z 2009-01 2008-05 Article http://purl.org/eprint/type/JournalArticle 00218693 http://hdl.handle.net/1721.1/96327 Etingof, Pavel, John Kim, and Xiaoguang Ma. “On Universal Lie Nilpotent Associative Algebras.” Journal of Algebra 321, no. 2 (January 2009): 697–703. © 2008 Elsevier Inc. https://orcid.org/0000-0002-0710-1416 en_US http://dx.doi.org/10.1016/j.jalgebra.2008.09.042 Journal of Algebra Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Elsevier B.V. Elsevier |
| spellingShingle | Etingof, Pavel I. Kim, John Ma, Xiaoguang On universal Lie nilpotent associative algebras |
| title | On universal Lie nilpotent associative algebras |
| title_full | On universal Lie nilpotent associative algebras |
| title_fullStr | On universal Lie nilpotent associative algebras |
| title_full_unstemmed | On universal Lie nilpotent associative algebras |
| title_short | On universal Lie nilpotent associative algebras |
| title_sort | on universal lie nilpotent associative algebras |
| url | http://hdl.handle.net/1721.1/96327 https://orcid.org/0000-0002-0710-1416 |
| work_keys_str_mv | AT etingofpaveli onuniversallienilpotentassociativealgebras AT kimjohn onuniversallienilpotentassociativealgebras AT maxiaoguang onuniversallienilpotentassociativealgebras |