Characterization of automorphisms of Hom-biproducts

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.

Keywords

• monoidal Hom-Hopf algebra,Hom-biproduct,automorphism

References

1. [1] N. Andruskiewitsch and H.J. Schneider, On the classification of finite-dimensional pointed Hopf algebras, Ann. Math. 171 (1), 375–417, 2010.
2. [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. [3] S. Caenepeel and I. Goyvaerts, Monoidal Hom-Hopf algebras, Comm. Alg. 39 (6), 2216–2240, 2011.
4. [4] Q.G. Chen and D.G.Wang, Constructing Quasitriangular Hopf Algebras, Comm. Alg. 43 (4), 1698–1722, 2015.
5. [5] Q.G. Chen and D.G. Wang, A Class of Coquasitriangular Hopf Group Algebras, Comm. Alg. 44 (1), 310–335, 2016.
6. [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. [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. [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. [9] L. Delvaux, Multiplier Hopf algebras in categories and the biproduct construction, Algebr. Represent. Theory, 10 (6), 533–554, 2007.
10. [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. [11] A. Gohr, On Hom-algebras with surjective twisting, J. Algebra, 324 (7), 1483–1491, 2010.
12. [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. [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. [14] A. Makhlouf and F. Panaite, Yetter-Drinfeld modules for Hom-bialgebras, J. Math. Phys. 55 (1), 013501, 2014.
15. [15] A. Makhlouf and S.D. Silvestrov, Hom-algebras structures, J. Gen. Lie Theory Appl. 2 (2), 51–64, 2008.
16. [16] A. Makhlouf and S.D. Silvestrov, Hom-algebras and Hom-coalgebras, J. Algebra Appl. 9 (4), 553–589, 2010.
17. [17] D.E. Radford, On automorphisms of biproducts, Comm. Alg. 45(4), 1365–1398, 2017.
18. [18] D. Yau, Hom-algebras and homology, J. Lie Theory, 19 (2), 409–421, 2009.
19. [19] D. Yau, Hom-bialgebras and comodule algebras, Int. Electron. J. Algebra, 8, 45–64, 2010.
20. [20] X.F. Zhao and X.H. Zhang, Lazy 2-cocycles over monoidal Hom-Hopf algebras, Colloq. Math. 142 (1), 61–81, 2016.