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dc.contributor.author
Rubio y Degrassi, Lleonard  
dc.contributor.author
Schroll, Sibylle  
dc.contributor.author
Solotar, Andrea Leonor  
dc.date.available
2023-10-11T19:02:20Z  
dc.date.issued
2022-09  
dc.identifier.citation
Rubio y Degrassi, Lleonard; Schroll, Sibylle; Solotar, Andrea Leonor; The first Hochschild cohomology as a Lie algebra; National Inquiry Services Centre; Quaestiones Mathematicae; 46; 9; 9-2022; 1955-1980  
dc.identifier.issn
1607-3606  
dc.identifier.uri
http://hdl.handle.net/11336/214932  
dc.description.abstract
In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, we show that if the quiver has no parallel arrows and no loops then the first Hochschild cohomology is solvable. For quivers containing loops, we determine easily verifiable sufficient conditions for the solvability of the first Hochschild cohomology. We apply these criteria to show the solvability of the first Hochschild cohomology space for large families of algebras, namely, several families of self-injective tame algebras including all tame blocks of finite groups and some wild algebras including most quantum complete intersections.  
dc.format
application/pdf  
dc.language.iso
eng  
dc.publisher
National Inquiry Services Centre  
dc.rights
info:eu-repo/semantics/restrictedAccess  
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/  
dc.subject
GERSTENHABER BRACKET  
dc.subject
HOCHSCHILD COHOMOLOGY  
dc.subject
LIE ALGEBRAS  
dc.subject
QUANTUM COMPLETE INTERSECTIONS  
dc.subject
SOLVABLE LIE ALGEBRAS  
dc.subject
SYMMETRIC ALGEBRAS  
dc.subject.classification
Matemática Pura  
dc.subject.classification
Matemáticas  
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS  
dc.title
The first Hochschild cohomology as a Lie algebra  
dc.type
info:eu-repo/semantics/article  
dc.type
info:ar-repo/semantics/artículo  
dc.type
info:eu-repo/semantics/publishedVersion  
dc.date.updated
2023-07-07T22:44:12Z  
dc.journal.volume
46  
dc.journal.number
9  
dc.journal.pagination
1955-1980  
dc.journal.pais
Sudáfrica  
dc.journal.ciudad
Johannesburg  
dc.description.fil
Fil: Rubio y Degrassi, Lleonard. Universita Degli Studi Di Verona; Italia  
dc.description.fil
Fil: Schroll, Sibylle. Universitat zu Köln; Alemania  
dc.description.fil
Fil: Solotar, Andrea Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina  
dc.journal.title
Quaestiones Mathematicae  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.2989/16073606.2022.2115424  
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.2989/16073606.2022.2115424