Characterization of automorphisms of Hom-biproducts
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.
___
- [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.