Loading…
Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type
Let A m , n be the tensor product of the polynomial algebra in m even variables and the exterior algebra in n odd variables over the complex field ℂ , and the Witt superalgebra W m , n be the Lie superalgebra of superderivations of A m , n . In this paper, we classify the non-trivial simple bounded...
Saved in:
| Published in: | Algebras and representation theory 2023-06, Vol.26 (3), p.763-781 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| 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-c319t-6226e69ccbcedd7be7c6bf5beb345bbb1fa3cf78a4ee82ba0000bf308ffe2b8f3 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c319t-6226e69ccbcedd7be7c6bf5beb345bbb1fa3cf78a4ee82ba0000bf308ffe2b8f3 |
| container_end_page | 781 |
| container_issue | 3 |
| container_start_page | 763 |
| container_title | Algebras and representation theory |
| container_volume | 26 |
| creator | Lü, Rencai Xue, Yaohui |
| description | Let
A
m
,
n
be the tensor product of the polynomial algebra in
m
even variables and the exterior algebra in
n
odd variables over the complex field
ℂ
, and the Witt superalgebra
W
m
,
n
be the Lie superalgebra of superderivations of
A
m
,
n
. In this paper, we classify the non-trivial simple bounded weight
W
m
,
n
modules with respect to the standard Cartan subalgebra of
W
m
,
n
. Any such module is a simple quotient of a tensor module
F
(
P
,
L
(
V
1
⊗
V
2
)) for a simple weight module
P
over the Weyl superalgebra
K
m
,
n
, a finite-dimensional simple
g
l
m
-module
V
1
and a simple bounded
g
l
n
-module
V
2
. |
| doi_str_mv | 10.1007/s10468-021-10112-3 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2818173631</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2818173631</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-6226e69ccbcedd7be7c6bf5beb345bbb1fa3cf78a4ee82ba0000bf308ffe2b8f3</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EEuXxA6wssTZ47NZ2lqXiJRV1AajsLDsZ96GSBDtB6t9jCBI7VjOLe-6MDiEXwK-Ac32dgI-VYVwAAw4gmDwgI5howQqui8O8S6NYIeTbMTlJacs5L5SBEZneNH1dYUWXuFmtO_rUVP0OE118YqTdGul8g_S5bzG63Qp9dLQJdOZi52q6ZN2-xTNyFNwu4fnvPCWvd7cvswc2X9w_zqZzVkooOqaEUKiKsvQlVpX2qEvlw8Sjl-OJ9x6Ck2XQxo0RjfAuf8h9kNyEgMKbIE_J5dDbxuajx9TZbdPHOp-0woABLZWEnBJDqoxNShGDbePm3cW9BW6_VdlBlc2q7I8qKzMkByjlcL3C-Ff9D_UFwsVsUw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2818173631</pqid></control><display><type>article</type><title>Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type</title><source>Springer Nature</source><creator>Lü, Rencai ; Xue, Yaohui</creator><creatorcontrib>Lü, Rencai ; Xue, Yaohui</creatorcontrib><description>Let
A
m
,
n
be the tensor product of the polynomial algebra in
m
even variables and the exterior algebra in
n
odd variables over the complex field
ℂ
, and the Witt superalgebra
W
m
,
n
be the Lie superalgebra of superderivations of
A
m
,
n
. In this paper, we classify the non-trivial simple bounded weight
W
m
,
n
modules with respect to the standard Cartan subalgebra of
W
m
,
n
. Any such module is a simple quotient of a tensor module
F
(
P
,
L
(
V
1
⊗
V
2
)) for a simple weight module
P
over the Weyl superalgebra
K
m
,
n
, a finite-dimensional simple
g
l
m
-module
V
1
and a simple bounded
g
l
n
-module
V
2
.</description><identifier>ISSN: 1386-923X</identifier><identifier>EISSN: 1572-9079</identifier><identifier>DOI: 10.1007/s10468-021-10112-3</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Associative Rings and Algebras ; Commutative Rings and Algebras ; Complex variables ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Modules ; Non-associative Rings and Algebras ; Polynomials ; Tensors</subject><ispartof>Algebras and representation theory, 2023-06, Vol.26 (3), p.763-781</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-6226e69ccbcedd7be7c6bf5beb345bbb1fa3cf78a4ee82ba0000bf308ffe2b8f3</citedby><cites>FETCH-LOGICAL-c319t-6226e69ccbcedd7be7c6bf5beb345bbb1fa3cf78a4ee82ba0000bf308ffe2b8f3</cites><orcidid>0000-0001-5985-544X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Lü, Rencai</creatorcontrib><creatorcontrib>Xue, Yaohui</creatorcontrib><title>Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type</title><title>Algebras and representation theory</title><addtitle>Algebr Represent Theor</addtitle><description>Let
A
m
,
n
be the tensor product of the polynomial algebra in
m
even variables and the exterior algebra in
n
odd variables over the complex field
ℂ
, and the Witt superalgebra
W
m
,
n
be the Lie superalgebra of superderivations of
A
m
,
n
. In this paper, we classify the non-trivial simple bounded weight
W
m
,
n
modules with respect to the standard Cartan subalgebra of
W
m
,
n
. Any such module is a simple quotient of a tensor module
F
(
P
,
L
(
V
1
⊗
V
2
)) for a simple weight module
P
over the Weyl superalgebra
K
m
,
n
, a finite-dimensional simple
g
l
m
-module
V
1
and a simple bounded
g
l
n
-module
V
2
.</description><subject>Associative Rings and Algebras</subject><subject>Commutative Rings and Algebras</subject><subject>Complex variables</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Modules</subject><subject>Non-associative Rings and Algebras</subject><subject>Polynomials</subject><subject>Tensors</subject><issn>1386-923X</issn><issn>1572-9079</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEuXxA6wssTZ47NZ2lqXiJRV1AajsLDsZ96GSBDtB6t9jCBI7VjOLe-6MDiEXwK-Ac32dgI-VYVwAAw4gmDwgI5howQqui8O8S6NYIeTbMTlJacs5L5SBEZneNH1dYUWXuFmtO_rUVP0OE118YqTdGul8g_S5bzG63Qp9dLQJdOZi52q6ZN2-xTNyFNwu4fnvPCWvd7cvswc2X9w_zqZzVkooOqaEUKiKsvQlVpX2qEvlw8Sjl-OJ9x6Ck2XQxo0RjfAuf8h9kNyEgMKbIE_J5dDbxuajx9TZbdPHOp-0woABLZWEnBJDqoxNShGDbePm3cW9BW6_VdlBlc2q7I8qKzMkByjlcL3C-Ff9D_UFwsVsUw</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Lü, Rencai</creator><creator>Xue, Yaohui</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-5985-544X</orcidid></search><sort><creationdate>20230601</creationdate><title>Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type</title><author>Lü, Rencai ; Xue, Yaohui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-6226e69ccbcedd7be7c6bf5beb345bbb1fa3cf78a4ee82ba0000bf308ffe2b8f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Associative Rings and Algebras</topic><topic>Commutative Rings and Algebras</topic><topic>Complex variables</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Modules</topic><topic>Non-associative Rings and Algebras</topic><topic>Polynomials</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lü, Rencai</creatorcontrib><creatorcontrib>Xue, Yaohui</creatorcontrib><collection>CrossRef</collection><jtitle>Algebras and representation theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lü, Rencai</au><au>Xue, Yaohui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type</atitle><jtitle>Algebras and representation theory</jtitle><stitle>Algebr Represent Theor</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>26</volume><issue>3</issue><spage>763</spage><epage>781</epage><pages>763-781</pages><issn>1386-923X</issn><eissn>1572-9079</eissn><abstract>Let
A
m
,
n
be the tensor product of the polynomial algebra in
m
even variables and the exterior algebra in
n
odd variables over the complex field
ℂ
, and the Witt superalgebra
W
m
,
n
be the Lie superalgebra of superderivations of
A
m
,
n
. In this paper, we classify the non-trivial simple bounded weight
W
m
,
n
modules with respect to the standard Cartan subalgebra of
W
m
,
n
. Any such module is a simple quotient of a tensor module
F
(
P
,
L
(
V
1
⊗
V
2
)) for a simple weight module
P
over the Weyl superalgebra
K
m
,
n
, a finite-dimensional simple
g
l
m
-module
V
1
and a simple bounded
g
l
n
-module
V
2
.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10468-021-10112-3</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0001-5985-544X</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1386-923X |
| ispartof | Algebras and representation theory, 2023-06, Vol.26 (3), p.763-781 |
| issn | 1386-923X 1572-9079 |
| language | eng |
| recordid | cdi_proquest_journals_2818173631 |
| source | Springer Nature |
| subjects | Associative Rings and Algebras Commutative Rings and Algebras Complex variables Mathematical analysis Mathematics Mathematics and Statistics Modules Non-associative Rings and Algebras Polynomials Tensors |
| title | Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T04%3A45%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Bounded%20Weight%20Modules%20Over%20the%20Lie%20Superalgebra%20of%20Cartan%20W-type&rft.jtitle=Algebras%20and%20representation%20theory&rft.au=L%C3%BC,%20Rencai&rft.date=2023-06-01&rft.volume=26&rft.issue=3&rft.spage=763&rft.epage=781&rft.pages=763-781&rft.issn=1386-923X&rft.eissn=1572-9079&rft_id=info:doi/10.1007/s10468-021-10112-3&rft_dat=%3Cproquest_cross%3E2818173631%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c319t-6226e69ccbcedd7be7c6bf5beb345bbb1fa3cf78a4ee82ba0000bf308ffe2b8f3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2818173631&rft_id=info:pmid/&rfr_iscdi=true |