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Characterization of automorphisms of Hom-biproducts

Year 2020, Volume: 49 Issue: 1, 147 - 161, 06.02.2020
https://doi.org/10.15672/HJMS.2019.668

Abstract

We study certain subgroups of the full group of monoidal Hom-Hopf algebra automorphisms of a Hom-biproduct, which gives a Hom-version of Radford’s results.

References

  • [1] N. Andruskiewitsch and H.J. Schneider, On the classification of finite-dimensional pointed Hopf algebras, Ann. Math. 171 (1), 375–417, 2010.
  • [2] D. Bulacu and E. Nauwelaerts, Radford’s biproduct for quasi-Hopf algebras and bosonization, J. Pure Appl. Algebra, 174 (1), 1–42, 2002.
  • [3] S. Caenepeel and I. Goyvaerts, Monoidal Hom-Hopf algebras, Comm. Alg. 39 (6), 2216–2240, 2011.
  • [4] Q.G. Chen and D.G.Wang, Constructing Quasitriangular Hopf Algebras, Comm. Alg. 43 (4), 1698–1722, 2015.
  • [5] Q.G. Chen and D.G. Wang, A Class of Coquasitriangular Hopf Group Algebras, Comm. Alg. 44 (1), 310–335, 2016.
  • [6] Q.G. Chen and D.G. Wang, Duality theorem for L-R crossed coproducts, Appl. Math. J. Chinese Univ. Ser. A, 33 (3), 359–378, 2018.
  • [7] Q.G. Chen and D.G. Wang, Hom-coalgebra cleft extensions and braided tensor Hom- categories of Hom-entwining structures , Hacet. J. Math. Stat. 48 (1), 1–15, 2019.
  • [8] Q.G. Chen, D.G. Wang and X.D. Kang, Twisted partial coactions of Hopf algebras, Front. Math. China, 12 (1), 63–86, 2017.
  • [9] L. Delvaux, Multiplier Hopf algebras in categories and the biproduct construction, Algebr. Represent. Theory, 10 (6), 533–554, 2007.
  • [10] Y. Fregier, A. Gohr and S.D. Silvestrov, Unital algebras of Hom-associative type and surjective or injective twistings, J. Gen. Lie Theory Appl. 3 (4), 285–295, 2009.
  • [11] A. Gohr, On Hom-algebras with surjective twisting, J. Algebra, 324 (7), 1483–1491, 2010.
  • [12] S.J. Guo, X.H. Zhang and S.X. Wang, Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras, Colloq. Math. 143 (1), 79–103, 2016.
  • [13] L. Liu and B.L. Shen, Radford’s biproducts and Yetter-Drinfeld modules for monoidal Hom-Hopf algebras, J. Math. Phys. 55 (3), 031701, 2014.
  • [14] A. Makhlouf and F. Panaite, Yetter-Drinfeld modules for Hom-bialgebras, J. Math. Phys. 55 (1), 013501, 2014.
  • [15] A. Makhlouf and S.D. Silvestrov, Hom-algebras structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008.
  • [16] A. Makhlouf and S.D. Silvestrov, Hom-algebras and Hom-coalgebras, J. Algebra Appl. 9 (4), 553–589, 2010.
  • [17] D.E. Radford, On automorphisms of biproducts, Comm. Alg. 45(4), 1365–1398, 2017.
  • [18] D. Yau, Hom-algebras and homology, J. Lie Theory, 19 (2), 409–421, 2009.
  • [19] D. Yau, Hom-bialgebras and comodule algebras, Int. Electron. J. Algebra, 8, 45–64, 2010.
  • [20] X.F. Zhao and X.H. Zhang, Lazy 2-cocycles over monoidal Hom-Hopf algebras, Colloq. Math. 142 (1), 61–81, 2016.
Year 2020, Volume: 49 Issue: 1, 147 - 161, 06.02.2020
https://doi.org/10.15672/HJMS.2019.668

Abstract

References

  • [1] N. Andruskiewitsch and H.J. Schneider, On the classification of finite-dimensional pointed Hopf algebras, Ann. Math. 171 (1), 375–417, 2010.
  • [2] D. Bulacu and E. Nauwelaerts, Radford’s biproduct for quasi-Hopf algebras and bosonization, J. Pure Appl. Algebra, 174 (1), 1–42, 2002.
  • [3] S. Caenepeel and I. Goyvaerts, Monoidal Hom-Hopf algebras, Comm. Alg. 39 (6), 2216–2240, 2011.
  • [4] Q.G. Chen and D.G.Wang, Constructing Quasitriangular Hopf Algebras, Comm. Alg. 43 (4), 1698–1722, 2015.
  • [5] Q.G. Chen and D.G. Wang, A Class of Coquasitriangular Hopf Group Algebras, Comm. Alg. 44 (1), 310–335, 2016.
  • [6] Q.G. Chen and D.G. Wang, Duality theorem for L-R crossed coproducts, Appl. Math. J. Chinese Univ. Ser. A, 33 (3), 359–378, 2018.
  • [7] Q.G. Chen and D.G. Wang, Hom-coalgebra cleft extensions and braided tensor Hom- categories of Hom-entwining structures , Hacet. J. Math. Stat. 48 (1), 1–15, 2019.
  • [8] Q.G. Chen, D.G. Wang and X.D. Kang, Twisted partial coactions of Hopf algebras, Front. Math. China, 12 (1), 63–86, 2017.
  • [9] L. Delvaux, Multiplier Hopf algebras in categories and the biproduct construction, Algebr. Represent. Theory, 10 (6), 533–554, 2007.
  • [10] Y. Fregier, A. Gohr and S.D. Silvestrov, Unital algebras of Hom-associative type and surjective or injective twistings, J. Gen. Lie Theory Appl. 3 (4), 285–295, 2009.
  • [11] A. Gohr, On Hom-algebras with surjective twisting, J. Algebra, 324 (7), 1483–1491, 2010.
  • [12] S.J. Guo, X.H. Zhang and S.X. Wang, Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras, Colloq. Math. 143 (1), 79–103, 2016.
  • [13] L. Liu and B.L. Shen, Radford’s biproducts and Yetter-Drinfeld modules for monoidal Hom-Hopf algebras, J. Math. Phys. 55 (3), 031701, 2014.
  • [14] A. Makhlouf and F. Panaite, Yetter-Drinfeld modules for Hom-bialgebras, J. Math. Phys. 55 (1), 013501, 2014.
  • [15] A. Makhlouf and S.D. Silvestrov, Hom-algebras structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008.
  • [16] A. Makhlouf and S.D. Silvestrov, Hom-algebras and Hom-coalgebras, J. Algebra Appl. 9 (4), 553–589, 2010.
  • [17] D.E. Radford, On automorphisms of biproducts, Comm. Alg. 45(4), 1365–1398, 2017.
  • [18] D. Yau, Hom-algebras and homology, J. Lie Theory, 19 (2), 409–421, 2009.
  • [19] D. Yau, Hom-bialgebras and comodule algebras, Int. Electron. J. Algebra, 8, 45–64, 2010.
  • [20] X.F. Zhao and X.H. Zhang, Lazy 2-cocycles over monoidal Hom-Hopf algebras, Colloq. Math. 142 (1), 61–81, 2016.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Quanguo Chen 0000-0002-8167-1070

Fu Tingting This is me 0000-0003-0056-8424

Publication Date February 6, 2020
Published in Issue Year 2020 Volume: 49 Issue: 1

Cite

APA Chen, Q., & Tingting, F. (2020). Characterization of automorphisms of Hom-biproducts. Hacettepe Journal of Mathematics and Statistics, 49(1), 147-161. https://doi.org/10.15672/HJMS.2019.668
AMA Chen Q, Tingting F. Characterization of automorphisms of Hom-biproducts. Hacettepe Journal of Mathematics and Statistics. February 2020;49(1):147-161. doi:10.15672/HJMS.2019.668
Chicago Chen, Quanguo, and Fu Tingting. “Characterization of Automorphisms of Hom-Biproducts”. Hacettepe Journal of Mathematics and Statistics 49, no. 1 (February 2020): 147-61. https://doi.org/10.15672/HJMS.2019.668.
EndNote Chen Q, Tingting F (February 1, 2020) Characterization of automorphisms of Hom-biproducts. Hacettepe Journal of Mathematics and Statistics 49 1 147–161.
IEEE Q. Chen and F. Tingting, “Characterization of automorphisms of Hom-biproducts”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, pp. 147–161, 2020, doi: 10.15672/HJMS.2019.668.
ISNAD Chen, Quanguo - Tingting, Fu. “Characterization of Automorphisms of Hom-Biproducts”. Hacettepe Journal of Mathematics and Statistics 49/1 (February 2020), 147-161. https://doi.org/10.15672/HJMS.2019.668.
JAMA Chen Q, Tingting F. Characterization of automorphisms of Hom-biproducts. Hacettepe Journal of Mathematics and Statistics. 2020;49:147–161.
MLA Chen, Quanguo and Fu Tingting. “Characterization of Automorphisms of Hom-Biproducts”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 1, 2020, pp. 147-61, doi:10.15672/HJMS.2019.668.
Vancouver Chen Q, Tingting F. Characterization of automorphisms of Hom-biproducts. Hacettepe Journal of Mathematics and Statistics. 2020;49(1):147-61.