Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve

Let H be the Radford Hopf algebra of dimension twelve over a field k . In this paper, we investigate the automorphism groups of the Green ring r ( H ) and the Green algebra ℂ( H ) ≔ ℂ ⊗ ℤ r ( H ) over the complex number field ℂ. The ring automorphisms of r ( H ) and the algebra automorphisms of ℂ( H...

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Bibliographic Details
Published in:Frontiers of Mathematics 2024-07, Vol.19 (4), p.691-710
Main Authors: Zhang, Xinru, Sun, Hua, Chen, Huixiang
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Research Article
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Summary:Let H be the Radford Hopf algebra of dimension twelve over a field k . In this paper, we investigate the automorphism groups of the Green ring r ( H ) and the Green algebra ℂ( H ) ≔ ℂ ⊗ ℤ r ( H ) over the complex number field ℂ. The ring automorphisms of r ( H ) and the algebra automorphisms of ℂ( H ) are all described. It is shown that the ring automorphism group of r ( H ) is isomorphic to the Klein group K 4 , and the algebra automorphism group of ℂ( H ) is isomorphic to the direct product ℂ x × S 4 , where ℂ x is the multiplicative group of all nonzero complex numbers and S 4 is the symmetric group of degree 4.
ISSN:2731-8648
2731-8656
DOI:10.1007/s11464-022-0293-x