Omni-representations of Leibniz algebras
Commun. Math. Res. 40 (2024), No. 1, 30-42 In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the omni-cohomology theory associa...
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| creator | Liu, Zhangju Sheng, Yunhe |
| description | Commun. Math. Res. 40 (2024), No. 1, 30-42 In this paper, first we introduce the notion of an omni-representation of a
Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism
from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the
omni-cohomology theory associated to omni-representations and establish the
relation between omni-cohomology groups and Loday-Pirashvili cohomology groups. |
| doi_str_mv | 10.48550/arxiv.2304.02809 |
| format | Article |
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Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism
from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the
omni-cohomology theory associated to omni-representations and establish the
relation between omni-cohomology groups and Loday-Pirashvili cohomology groups.</description><identifier>DOI: 10.48550/arxiv.2304.02809</identifier><language>eng</language><subject>Mathematics - Representation Theory ; Mathematics - Rings and Algebras</subject><creationdate>2023-04</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2304.02809$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2304.02809$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Zhangju</creatorcontrib><creatorcontrib>Sheng, Yunhe</creatorcontrib><title>Omni-representations of Leibniz algebras</title><description>Commun. Math. Res. 40 (2024), No. 1, 30-42 In this paper, first we introduce the notion of an omni-representation of a
Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism
from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the
omni-cohomology theory associated to omni-representations and establish the
relation between omni-cohomology groups and Loday-Pirashvili cohomology groups.</description><subject>Mathematics - Representation Theory</subject><subject>Mathematics - Rings and Algebras</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrsKwjAUgOEsDqI-gJMdXVqPSZqcjCLeoODiXk7JiQS0SiqiPr14mf7t5xNiPIdCY1nCjNIj3gupQBcgEVxfTPfnNuaJr4k7bm90i5e2yy4hqzg2bXxldDpyk6gbil6gU8ejfwfisF4dltu82m92y0WVk7Eux6AkKN9Ycgql0chWojfsvQZDXgJj4yBYK9nwXHLJLhCxRmsdAJZqICa_7ZdaX1M8U3rWH3L9Jas39N860w</recordid><startdate>20230405</startdate><enddate>20230405</enddate><creator>Liu, Zhangju</creator><creator>Sheng, Yunhe</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230405</creationdate><title>Omni-representations of Leibniz algebras</title><author>Liu, Zhangju ; Sheng, Yunhe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-8f3203db7a9382648e728d6edd406ad20e8b90f772e6e12e5e9faae4877900853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Representation Theory</topic><topic>Mathematics - Rings and Algebras</topic><toplevel>online_resources</toplevel><creatorcontrib>Liu, Zhangju</creatorcontrib><creatorcontrib>Sheng, Yunhe</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Liu, Zhangju</au><au>Sheng, Yunhe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Omni-representations of Leibniz algebras</atitle><date>2023-04-05</date><risdate>2023</risdate><abstract>Commun. Math. Res. 40 (2024), No. 1, 30-42 In this paper, first we introduce the notion of an omni-representation of a
Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism
from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the
omni-cohomology theory associated to omni-representations and establish the
relation between omni-cohomology groups and Loday-Pirashvili cohomology groups.</abstract><doi>10.48550/arxiv.2304.02809</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Representation Theory Mathematics - Rings and Algebras |
| title | Omni-representations of Leibniz algebras |
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