Yıl 2018, Cilt 24, Sayı 24, Sayfalar 174 - 194 2018-07-05

HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS

Per Back [1] , Johan Richter [2] , Sergei Silvestrov [3]

25 38

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, andWeyl 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 homassociative
algebra into a multiplicative, weakly unital hom-associative algebra,
which we call a weak unitalization.
Hom-associative Ore extensions, hom-associative Weyl algebras
  • N. Aizawa and H. Sato, q-deformation of the Virasoro algebra with central ex- tension, Phys. Lett. B, 256(2) (1991), 185-190 (Preprint Hiroshima University HUPD-9012 (1990)).
  • M. Chaichian, D. Ellinas and Z. Popowicz, Quantum conformal algebra with central extension, Phys. Lett. B, 248 (1990), 95-99.
  • M. Chaichian, A. P. Isaev, J. Lukierski, Z. Popowic and P. Presnajder, q- deformations of Virasoro algebra and conformal dimensions, Phys. Lett. B, 262(1) (1991), 32-38.
  • M. Chaichian, P. Kulish and J. Lukierski, q-deformed Jacobi identity, q- oscillators and q-deformed in nite-dimensional algebras, Phys. Lett. B, 237(3- 4) (1990), 401-406.
  • M. Chaichian, Z. Popowicz and P. Presnajder, q-Virasoro algebra and its re- lation to the q-deformed KdV system, Phys. Lett. B, 249(1) (1990), 63-65.
  • T. L. Curtright and C. K. Zachos, Deforming maps for quantum algebras, Phys. Lett. B, 243(3) (1990), 237-244.
  • T. L. Curtright, D. B. Fairlie and C. K. Zachos, Ternary Virasoro-Witt algebra, Phys. Lett. B, 666(4) (2008), 386-390.
  • C. Daskaloyannis, Generalized deformed Virasoro algebras, Modern Phys. Lett. A, 7(9) (1992), 809-816.
  • Y. Fregier and A. Gohr, On unitality conditions for Hom-associative algebras, arXiv:0904.4874 (2009).
  • J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using -derivations, J. Algebra, 295(2) (2006), 314-361 (Preprint Lund University LUTFMA-5036-2003 (2003)).
  • N. Hu, q-Witt algebras, q-Lie algebras, q-holomorph structure and representa- tions, Algebra Colloq., 6(1) (1999), 51-70.
  • C. Kassel, Cyclic homology of di erential operators, the Virasoro algebra and a q-analogue, Comm. Math. Phys., 146(2) (1992), 343-356.
  • D. Larsson and S. D. Silvestrov, Quasi-Hom-Lie algebras, central extensions and 2-cocycle-like identities, J. Algebra, 288(2) (2005), 321-344 (Preprint Lund University LUTFMA-5038-2004 (2004)).
  • D. Larsson and S. D. Silvestrov, Quasi-Lie Algebras, in \Noncommutative geometry and representation theory in mathematical physics", eds. J. Fuchs, J. Mickelsson, G. Rozenblioum, A. Stolin, A. Westerberg, Amer. Math. Soc., Providence, RI, Contemp. Math., 391, (2005), 241-248. (Preprint Lund University LUTFMA-5049-2004 (2004)).
  • D. Larsson and S. D. Silvestrov, Graded quasi-Lie algebras, Czechoslovak J. Phys., 55(11) (2005), 1473-1478.
  • K. Q. Liu, Quantum central extensions, C. R. Math. Rep. Acad. Sci. Canada, 13 (1991), 135-140.
  • K. Q. Liu, Characterizations of the quantum Witt algebra, Lett. Math. Phys., 24(4) (1992), 257-265.
  • K. Q. Liu, The quantum Witt algebra and quantization of some modules over Witt algebra, PhD thesis, University of Alberta, 1992.
  • A. Makhlouf and S. D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2(2) (2008), 51-64 (Preprint Lund University LUTFMA-5074-2006 (2006)).
  • A. Makhlouf A and S. D. Silvestrov, Hom-Lie admissible hom-coalgebras and hom-Hopf algebras, in Generalized Lie Theory in Mathematics, Physics and Beyond, S. Silvestrov, E. Paal et al eds., Springer, Berlin, 2009, chapter 17 pp 189-206 (Preprint Lund University LUTFMA-5091-2007 (2007) and arXiv:0709.2413 (2007)).
  • A. Makhlouf and S. D. Silvestrov, Hom-algebras and hom-coalgebras, J. Algebra Appl., 9(4) (2010), 553-589 (Preprint Lund University LUTFMA-5103-2008 (2008) and arXiv:0811.0400 (2008))
  • P. Nystedt, A combinatorial proof of associativity of Ore extensions, Discrete Math., 313(23) (2013), 2748-2750.
  • P. Nystedt, J.  Oinert and J. Richter, Monoid Ore extensions, arXiv:1705.02778 (2017).
  • P. Nystedt, J.  Oinert and J. Richter, Non-associative Ore extensions, Isr. J. Math., 224(1) (2018), 263-292, arXiv:1509.01436 (2015).
  • G. Sigurdsson and S. D. Silvestrov, Graded quasi-Lie algebras of Witt type, Czech J Phys., 56(10-11) (2006), 1287-1291.
  • D. Yau, Hom-algebras and homology, J. Lie Theory, 19 (2009), 409-421.
Birincil Dil en
Konular Matematik
Dergi Bölümü Makaleler
Yazarlar

Yazar: Per Back

Yazar: Johan Richter

Yazar: Sergei Silvestrov (Sorumlu Yazar)

Bibtex @araştırma makalesi { ieja440245, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2018}, volume = {24}, pages = {174 - 194}, doi = {10.24330/ieja.440245}, title = {HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS}, key = {cite}, author = {Silvestrov, Sergei and Back, Per and Richter, Johan} }
APA Back, P , Richter, J , Silvestrov, S . (2018). HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS. International Electronic Journal of Algebra, 24 (24), 174-194. DOI: 10.24330/ieja.440245
MLA Back, P , Richter, J , Silvestrov, S . "HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS". International Electronic Journal of Algebra 24 (2018): 174-194 <http://dergipark.gov.tr/ieja/issue/38161/440245>
Chicago Back, P , Richter, J , Silvestrov, S . "HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS". International Electronic Journal of Algebra 24 (2018): 174-194
RIS TY - JOUR T1 - HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS AU - Per Back , Johan Richter , Sergei Silvestrov Y1 - 2018 PY - 2018 N1 - doi: 10.24330/ieja.440245 DO - 10.24330/ieja.440245 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 174 EP - 194 VL - 24 IS - 24 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.440245 UR - http://dx.doi.org/10.24330/ieja.440245 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS %A Per Back , Johan Richter , Sergei Silvestrov %T HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS %D 2018 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 24 %N 24 %R doi: 10.24330/ieja.440245 %U 10.24330/ieja.440245
ISNAD Back, Per , Richter, Johan , Silvestrov, Sergei . "HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS". International Electronic Journal of Algebra 24 / 24 (Temmuz 2018): 174-194. http://dx.doi.org/10.24330/ieja.440245