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Bäck, Per
Publications (3 of 3) Show all publications
Bäck, P. (2019). Notes on formal deformations of quantum planes and universal enveloping algebras. Paper presented at The 32nd International Colloquium on Group Theoretical Methods in Physics, Group32; Czech Technical University; Prague; Czech Republic; 9th July through 13th July, 2018.. Journal of Physics, Conference Series, 1194(1), Article ID 012011.
Open this publication in new window or tab >>Notes on formal deformations of quantum planes and universal enveloping algebras
2019 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 1194, no 1, article id 012011Article in journal (Refereed) Published
Abstract [en]

In these notes, we introduce formal hom-associative deformations of the quantumplanes and the universal enveloping algebras of the two-dimensional non-abelian Lie algebras.We then show that these deformations induce formal hom-Lie deformations of the correspondingLie algebras constructed by using the commutator as bracket.

Place, publisher, year, edition, pages
Institute of Physics Publishing, 2019
Keywords
Hom-associative algebras, hom-Lie algebras, hom-associative Ore extensions, hom-associative quantum planes, hom-associative universal enveloping algebras, hom-associative deformations, hom-Lie deformations
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-43409 (URN)10.1088/1742-6596/1194/1/012011 (DOI)2-s2.0-85065569764 (Scopus ID)
Conference
The 32nd International Colloquium on Group Theoretical Methods in Physics, Group32; Czech Technical University; Prague; Czech Republic; 9th July through 13th July, 2018.
Available from: 2019-05-09 Created: 2019-05-09 Last updated: 2019-05-24Bibliographically approved
Bäck, P., Richter, J. & Silvestrov, S. (2018). Hom-associative Ore extensions. Paper presented at 25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017; Czech Technical UniversityPrague; Czech Republic; 6 June 2017 through 10 June 2017; Code 134824. Journal of Physics, Conference Series, 965(1), Article ID 012006.
Open this publication in new window or tab >>Hom-associative Ore extensions
2018 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 965, no 1, article id 012006Article in journal (Refereed) Published
Abstract [en]

We introduce hom-associative Ore extensions as non-associative, non-unital Ore extensions with a hom-associative multiplication, as well as give some necessary and sufficient conditions when such exist. Within this framework, we also construct a family of hom-associative Weyl algebras as generalizations of the classical analogue, and prove that they are simple.

Place, publisher, year, edition, pages
Institute of Physics Publishing, 2018
National Category
Mathematics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-38849 (URN)10.1088/1742-6596/965/1/012006 (DOI)000446028000006 ()2-s2.0-85042922463 (Scopus ID)
Conference
25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017; Czech Technical UniversityPrague; Czech Republic; 6 June 2017 through 10 June 2017; Code 134824
Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2018-10-18Bibliographically approved
Bäck, P., Richter, J. & Silvestrov, S. (2018). Hom-associative Ore extensions and weak unitalizations. International Electronic Journal of Algebra, 24, 174-194
Open this publication in new window or tab >>Hom-associative Ore extensions and weak unitalizations
2018 (English)In: International Electronic Journal of Algebra, ISSN 1306-6048, E-ISSN 1306-6048, Vol. 24, p. 174-194Article in journal (Refereed) Published
Abstract [en]

We introduce hom-associative Ore extensions as non-unital, nonassociative Ore extensions with a hom-associative multiplication, and give some necessary and sucient conditions when such exist. Within this framework, we construct families of hom-associative quantum planes, universal enveloping algebras of a Lie algebra, and Weyl algebras, all being hom-associative generalizations of their classical counterparts, as well as prove that the latter are simple. We also provide a way of embedding any multiplicative hom-associative algebra into a multiplicative, weakly unital hom-associative algebra, which we call a weak unitalization.

Keywords
hom-associative Ore extensions, hom-associative Weyl algebras, hom-associative algebras
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-40202 (URN)10.24330/ieja.440245 (DOI)000438336600013 ()2-s2.0-85051115772 (Scopus ID)
Available from: 2018-07-05 Created: 2018-07-05 Last updated: 2018-08-16Bibliographically approved
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