SavedAdd your journal

Journals / International Electronic Journal of Algebra / 2018 / Volume: 24 Issue: 24

HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS

Per Back
Johan Richter
Sergei Silvestrov
Pages
—
Publication Date
2018-07-05
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We introduce hom-associative Ore extensions as non-unital, nonassociative

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce hom-associative Ore extensions as non-unital, nonassociative
📊
Key Findings & Data:We introduce hom-associative Ore extensions as non-unital, nonassociative
💡
Conclusion & Impact:We introduce hom-associative Ore extensions as non-unital, nonassociative
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hom-associative Ore extensions · hom-associative Weyl algebras

Abstract

We introduce hom-associative Ore extensions as non-unital, nonassociative

🔖

Cite This Article

Back, P., Richter, J., Silvestrov, S. (2018). HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS. International Electronic Journal of Algebra, Volume: 24 Issue: 24. https://doi.org/10.24330/ieja.440245

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (26)

  1. 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)).
  2. M. Chaichian, D. Ellinas and Z. Popowicz, Quantum conformal algebra with central extension, Phys. Lett. B, 248 (1990), 95-99.
  3. 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.
  4. 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.
  5. 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.
  6. T. L. Curtright and C. K. Zachos, Deforming maps for quantum algebras, Phys. Lett. B, 243(3) (1990), 237-244.
  7. T. L. Curtright, D. B. Fairlie and C. K. Zachos, Ternary Virasoro-Witt algebra, Phys. Lett. B, 666(4) (2008), 386-390.
  8. C. Daskaloyannis, Generalized deformed Virasoro algebras, Modern Phys. Lett. A, 7(9) (1992), 809-816.
  9. Y. Fregier and A. Gohr, On unitality conditions for Hom-associative algebras, arXiv:0904.4874 (2009).
  10. 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)).
  11. N. Hu, q-Witt algebras, q-Lie algebras, q-holomorph structure and representa- tions, Algebra Colloq., 6(1) (1999), 51-70.
  12. C. Kassel, Cyclic homology of di erential operators, the Virasoro algebra and a q-analogue, Comm. Math. Phys., 146(2) (1992), 343-356.
  13. 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)).
  14. 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)).
  15. D. Larsson and S. D. Silvestrov, Graded quasi-Lie algebras, Czechoslovak J. Phys., 55(11) (2005), 1473-1478.
  16. K. Q. Liu, Quantum central extensions, C. R. Math. Rep. Acad. Sci. Canada, 13 (1991), 135-140.
  17. K. Q. Liu, Characterizations of the quantum Witt algebra, Lett. Math. Phys., 24(4) (1992), 257-265.
  18. K. Q. Liu, The quantum Witt algebra and quantization of some modules over Witt algebra, PhD thesis, University of Alberta, 1992.
  19. 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)).
  20. 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)).
  21. 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))
  22. P. Nystedt, A combinatorial proof of associativity of Ore extensions, Discrete Math., 313(23) (2013), 2748-2750.
  23. P. Nystedt, J.  Oinert and J. Richter, Monoid Ore extensions, arXiv:1705.02778 (2017).
  24. P. Nystedt, J.  Oinert and J. Richter, Non-associative Ore extensions, Isr. J. Math., 224(1) (2018), 263-292, arXiv:1509.01436 (2015).
  25. G. Sigurdsson and S. D. Silvestrov, Graded quasi-Lie algebras of Witt type, Czech J Phys., 56(10-11) (2006), 1287-1291.
  26. D. Yau, Hom-algebras and homology, J. Lie Theory, 19 (2009), 409-421.