Research Article
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Year 2018, , 174 - 194, 05.07.2018
https://doi.org/10.24330/ieja.440245

Abstract

References

  • 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.

HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS

Year 2018, , 174 - 194, 05.07.2018
https://doi.org/10.24330/ieja.440245

Abstract

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.

References

  • 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.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Per Back This is me

Johan Richter This is me

Sergei Silvestrov

Publication Date July 5, 2018
Published in Issue Year 2018

Cite

APA Back, P., Richter, J., & Silvestrov, S. (2018). HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS. International Electronic Journal of Algebra, 24(24), 174-194. https://doi.org/10.24330/ieja.440245
AMA Back P, Richter J, Silvestrov S. HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS. IEJA. July 2018;24(24):174-194. doi:10.24330/ieja.440245
Chicago Back, Per, Johan Richter, and Sergei Silvestrov. “HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS”. International Electronic Journal of Algebra 24, no. 24 (July 2018): 174-94. https://doi.org/10.24330/ieja.440245.
EndNote Back P, Richter J, Silvestrov S (July 1, 2018) HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS. International Electronic Journal of Algebra 24 24 174–194.
IEEE P. Back, J. Richter, and S. Silvestrov, “HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS”, IEJA, vol. 24, no. 24, pp. 174–194, 2018, doi: 10.24330/ieja.440245.
ISNAD Back, Per et al. “HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS”. International Electronic Journal of Algebra 24/24 (July 2018), 174-194. https://doi.org/10.24330/ieja.440245.
JAMA Back P, Richter J, Silvestrov S. HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS. IEJA. 2018;24:174–194.
MLA Back, Per et al. “HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS”. International Electronic Journal of Algebra, vol. 24, no. 24, 2018, pp. 174-9, doi:10.24330/ieja.440245.
Vancouver Back P, Richter J, Silvestrov S. HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS. IEJA. 2018;24(24):174-9.