Lie algebras with differential operators of any weights

In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $...

Full description

Saved in:
Bibliographic Details
Published in:Electronic research archive 2023, Vol.31 (3), p.1195-1211
Main Authors: Li, Yizheng, Wang, Dingguo
Format: Article
Language:English
Subjects:
cohomology
deformation
derivation
extension
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c266t-d142a3c80908dc7b7a2812269b7736c2fa1b936dfa6c6c2e1897ae7008ada6ec3
cites cdi_FETCH-LOGICAL-c266t-d142a3c80908dc7b7a2812269b7736c2fa1b936dfa6c6c2e1897ae7008ada6ec3
container_end_page 1211
container_issue 3
container_start_page 1195
container_title Electronic research archive
container_volume 31
creator Li, Yizheng
Wang, Dingguo
description In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $ algebras and 2-differential operators of any weight on Lie 2-algebras, and we prove that the category of 2-term $ \mathrm{L}_{\infty} $ algebras with homotopy differential operators of any weight is same as the category of Lie 2-algebras with 2-differential operators of any weight.
doi_str_mv 10.3934/era.2023061
format article
fullrecord <record><control><sourceid>doaj_cross</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_7f194977c97a41918410d831fe7be8da</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_7f194977c97a41918410d831fe7be8da</doaj_id><sourcerecordid>oai_doaj_org_article_7f194977c97a41918410d831fe7be8da</sourcerecordid><originalsourceid>FETCH-LOGICAL-c266t-d142a3c80908dc7b7a2812269b7736c2fa1b936dfa6c6c2e1897ae7008ada6ec3</originalsourceid><addsrcrecordid>eNpN0MlKA0EQBuBGFAwxJ1-g7zKxerGXowSXQMCLnpuaXpIOYyZ0D4S8vaMJwVMth6-on5B7BnNhhXyMBeccuADFrsiEK2Ma9mTl9b_-lsxq3QIANwxAqgnRqxwpduvYFqz0kIcNDTmlWOJuyNjRfj-yQ18q7RPF3ZEeYl5vhnpHbhJ2Nc7OdUq-Xl8-F-_N6uNtuXheNZ4rNTSBSY7CG7BggtetxvEy58q2WgvleULWWqFCQuXHMTJjNUYNYDCgil5MyfLkhh63bl_yN5aj6zG7v0Vf1g7LkH0XnU7MSqu1HwnJLDOSQTCCpajbaAKO1sPJ8qWvtcR08Ri43wjd-Ks7Ryh-AHhJYwk</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Lie algebras with differential operators of any weights</title><source>Alma/SFX Local Collection</source><creator>Li, Yizheng ; Wang, Dingguo</creator><creatorcontrib>Li, Yizheng ; Wang, Dingguo</creatorcontrib><description>In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $ algebras and 2-differential operators of any weight on Lie 2-algebras, and we prove that the category of 2-term $ \mathrm{L}_{\infty} $ algebras with homotopy differential operators of any weight is same as the category of Lie 2-algebras with 2-differential operators of any weight.</description><identifier>ISSN: 2688-1594</identifier><identifier>EISSN: 2688-1594</identifier><identifier>DOI: 10.3934/era.2023061</identifier><language>eng</language><publisher>AIMS Press</publisher><subject>cohomology ; deformation ; derivation ; extension</subject><ispartof>Electronic research archive, 2023, Vol.31 (3), p.1195-1211</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c266t-d142a3c80908dc7b7a2812269b7736c2fa1b936dfa6c6c2e1897ae7008ada6ec3</citedby><cites>FETCH-LOGICAL-c266t-d142a3c80908dc7b7a2812269b7736c2fa1b936dfa6c6c2e1897ae7008ada6ec3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,4023,27922,27923,27924</link.rule.ids></links><search><creatorcontrib>Li, Yizheng</creatorcontrib><creatorcontrib>Wang, Dingguo</creatorcontrib><title>Lie algebras with differential operators of any weights</title><title>Electronic research archive</title><description>In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $ algebras and 2-differential operators of any weight on Lie 2-algebras, and we prove that the category of 2-term $ \mathrm{L}_{\infty} $ algebras with homotopy differential operators of any weight is same as the category of Lie 2-algebras with 2-differential operators of any weight.</description><subject>cohomology</subject><subject>deformation</subject><subject>derivation</subject><subject>extension</subject><issn>2688-1594</issn><issn>2688-1594</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>DOA</sourceid><recordid>eNpN0MlKA0EQBuBGFAwxJ1-g7zKxerGXowSXQMCLnpuaXpIOYyZ0D4S8vaMJwVMth6-on5B7BnNhhXyMBeccuADFrsiEK2Ma9mTl9b_-lsxq3QIANwxAqgnRqxwpduvYFqz0kIcNDTmlWOJuyNjRfj-yQ18q7RPF3ZEeYl5vhnpHbhJ2Nc7OdUq-Xl8-F-_N6uNtuXheNZ4rNTSBSY7CG7BggtetxvEy58q2WgvleULWWqFCQuXHMTJjNUYNYDCgil5MyfLkhh63bl_yN5aj6zG7v0Vf1g7LkH0XnU7MSqu1HwnJLDOSQTCCpajbaAKO1sPJ8qWvtcR08Ri43wjd-Ks7Ryh-AHhJYwk</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Li, Yizheng</creator><creator>Wang, Dingguo</creator><general>AIMS Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>DOA</scope></search><sort><creationdate>2023</creationdate><title>Lie algebras with differential operators of any weights</title><author>Li, Yizheng ; Wang, Dingguo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c266t-d142a3c80908dc7b7a2812269b7736c2fa1b936dfa6c6c2e1897ae7008ada6ec3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>cohomology</topic><topic>deformation</topic><topic>derivation</topic><topic>extension</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Yizheng</creatorcontrib><creatorcontrib>Wang, Dingguo</creatorcontrib><collection>CrossRef</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Electronic research archive</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Yizheng</au><au>Wang, Dingguo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lie algebras with differential operators of any weights</atitle><jtitle>Electronic research archive</jtitle><date>2023</date><risdate>2023</risdate><volume>31</volume><issue>3</issue><spage>1195</spage><epage>1211</epage><pages>1195-1211</pages><issn>2688-1594</issn><eissn>2688-1594</eissn><abstract>In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $ algebras and 2-differential operators of any weight on Lie 2-algebras, and we prove that the category of 2-term $ \mathrm{L}_{\infty} $ algebras with homotopy differential operators of any weight is same as the category of Lie 2-algebras with 2-differential operators of any weight.</abstract><pub>AIMS Press</pub><doi>10.3934/era.2023061</doi><tpages>17</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2688-1594
ispartof Electronic research archive, 2023, Vol.31 (3), p.1195-1211
issn 2688-1594
2688-1594
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_7f194977c97a41918410d831fe7be8da
source Alma/SFX Local Collection
subjects cohomology
deformation
derivation
extension
title Lie algebras with differential operators of any weights
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T15%3A58%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-doaj_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Lie%20algebras%20with%20differential%20operators%20of%20any%20weights&rft.jtitle=Electronic%20research%20archive&rft.au=Li,%20Yizheng&rft.date=2023&rft.volume=31&rft.issue=3&rft.spage=1195&rft.epage=1211&rft.pages=1195-1211&rft.issn=2688-1594&rft.eissn=2688-1594&rft_id=info:doi/10.3934/era.2023061&rft_dat=%3Cdoaj_cross%3Eoai_doaj_org_article_7f194977c97a41918410d831fe7be8da%3C/doaj_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c266t-d142a3c80908dc7b7a2812269b7736c2fa1b936dfa6c6c2e1897ae7008ada6ec3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true