On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries
We study the quantum vertex algebraic framework for the Yangians of RTT-type and the braided Yangians associated with Hecke symmetries, introduced by Gurevich and Saponov. First, we construct several families of modules for the aforementioned Yangian-like algebras which, in the RTT-type case, lead t...
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| Veröffentlicht in: | Communications in mathematical physics 2023, Vol.397 (2), p.607-634 |
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| creator | Slaven, Kožić |
| description | We study the quantum vertex algebraic framework for the Yangians of RTT-type and the braided Yangians associated with Hecke symmetries, introduced by Gurevich and Saponov. First, we construct several families of modules for the aforementioned Yangian-like algebras which, in the RTT-type case, lead to a certain
h
-adic quantum vertex algebra
V
c
(
R
)
via the Etingof–Kazhdan construction, while, in the braided case, they produce (
ϕ
-coordinated)
V
c
(
R
)
-modules. Next, we show that the coefficients of suitably defined quantum determinant can be used to obtain central elements of
V
c
(
R
)
, as well as the invariants of such (
ϕ
-coordinated)
V
c
(
R
)
-modules. Finally, we investigate a certain algebra which is closely connected with the representation theory of
V
c
(
R
)
. |
| doi_str_mv | 10.1007/s00220-022-04498-4 |
| format | Article |
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h
-adic quantum vertex algebra
V
c
(
R
)
via the Etingof–Kazhdan construction, while, in the braided case, they produce (
ϕ
-coordinated)
V
c
(
R
)
-modules. Next, we show that the coefficients of suitably defined quantum determinant can be used to obtain central elements of
V
c
(
R
)
, as well as the invariants of such (
ϕ
-coordinated)
V
c
(
R
)
-modules. Finally, we investigate a certain algebra which is closely connected with the representation theory of
V
c
(
R
)
.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-022-04498-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebra ; Braiding ; Classical and Quantum Gravitation ; Complex Systems ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematical Physics ; Modules ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Communications in mathematical physics, 2023, Vol.397 (2), p.607-634</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-9c0db2645450c6306f4553d3d0dc2f09126ba30f9fca32fd8c6e9aa21f1640f33</cites><orcidid>0000-0003-2276-3271</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00220-022-04498-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00220-022-04498-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Slaven, Kožić</creatorcontrib><title>On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>We study the quantum vertex algebraic framework for the Yangians of RTT-type and the braided Yangians associated with Hecke symmetries, introduced by Gurevich and Saponov. First, we construct several families of modules for the aforementioned Yangian-like algebras which, in the RTT-type case, lead to a certain
h
-adic quantum vertex algebra
V
c
(
R
)
via the Etingof–Kazhdan construction, while, in the braided case, they produce (
ϕ
-coordinated)
V
c
(
R
)
-modules. Next, we show that the coefficients of suitably defined quantum determinant can be used to obtain central elements of
V
c
(
R
)
, as well as the invariants of such (
ϕ
-coordinated)
V
c
(
R
)
-modules. Finally, we investigate a certain algebra which is closely connected with the representation theory of
V
c
(
R
)
.</description><subject>Algebra</subject><subject>Braiding</subject><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Modules</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKt_wFXAdfTmMWlnWYq1QqGIj21I82indmZqksH23xsdwZ2bc7nwnXMvB6FrCrcUYHQXARgDkoWAEOWYiBM0oILntaTyFA0AKBAuqTxHFzFuAaBkUg7QbNngtHF4Q7StDH7qdJO6Gr-5kNwBT3Zrtwo64kmMral0chZ_VmmD5868O_x8rGuXQuXiJTrzehfd1e8cotfZ_ct0ThbLh8fpZEEMG0EipQG7YlIUogAjOUgvioJbbsEa5vOrTK40B196oznzdmykK7Vm1FMpwHM-RDd97j60H52LSW3bLjT5pGIjWbICoIBMsZ4yoY0xOK_2oap1OCoK6rsv1felsqifvpTIJt6bYoabtQt_0f-4vgC3-Ww3</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Slaven, Kožić</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-2276-3271</orcidid></search><sort><creationdate>2023</creationdate><title>On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries</title><author>Slaven, Kožić</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-9c0db2645450c6306f4553d3d0dc2f09126ba30f9fca32fd8c6e9aa21f1640f33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Braiding</topic><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Modules</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Slaven, Kožić</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Slaven, Kožić</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2023</date><risdate>2023</risdate><volume>397</volume><issue>2</issue><spage>607</spage><epage>634</epage><pages>607-634</pages><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>We study the quantum vertex algebraic framework for the Yangians of RTT-type and the braided Yangians associated with Hecke symmetries, introduced by Gurevich and Saponov. First, we construct several families of modules for the aforementioned Yangian-like algebras which, in the RTT-type case, lead to a certain
h
-adic quantum vertex algebra
V
c
(
R
)
via the Etingof–Kazhdan construction, while, in the braided case, they produce (
ϕ
-coordinated)
V
c
(
R
)
-modules. Next, we show that the coefficients of suitably defined quantum determinant can be used to obtain central elements of
V
c
(
R
)
, as well as the invariants of such (
ϕ
-coordinated)
V
c
(
R
)
-modules. Finally, we investigate a certain algebra which is closely connected with the representation theory of
V
c
(
R
)
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-022-04498-4</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0003-2276-3271</orcidid></addata></record> |
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| ispartof | Communications in mathematical physics, 2023, Vol.397 (2), p.607-634 |
| issn | 0010-3616 1432-0916 |
| language | eng |
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| subjects | Algebra Braiding Classical and Quantum Gravitation Complex Systems Mathematical analysis Mathematical and Computational Physics Mathematical Physics Modules Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical |
| title | On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries |
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