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http://hdl.handle.net/1942/30586
Title: | Bilinear Forms on the Green Rings of Finite Dimensional Hopf Algebras | Authors: | WANG, Zhihua Li, Libin ZHANG, Yinhuo |
Issue Date: | 2019 | Publisher: | SPRINGER | Source: | ALGEBRAS AND REPRESENTATION THEORY, 22 (6) , p. 1569 -1598 | Abstract: | In this paper, we study the Green ring and the stable Green ring of a finite dimensional Hopf algebra by means of bilinear forms. We show that the Green ring of a Hopf algebra of finite representation type is a Frobenius algebra over Z with a dual basis associated to almost split sequences. On the stable Green ring we define a new bilinear form which is more accurate to determine the bi-Frobenius algebra structure on the stable Green ring. We show that the complexified stable Green algebra is a group-like algebra, and hence a bi-Frobenius algebra, if the bilinear form on the stable Green ring is non-degenerate. | Notes: | Wang, ZH (reprint author), Taizhou Univ, Dept Math, Taizhou 225300, Peoples R China. mailzhihua@126.com; lbli@yzu.edu.cn; yinhuo.zhang@uhasselt.be |
Other: | Wang, ZH (reprint author), Taizhou Univ, Dept Math, Taizhou 225300, Peoples R China. mailzhihua@126.com; lbli@yzu.edu.cn; yinhuo.zhang@uhasselt.be | Keywords: | Green ring;Stable Green ring;Grothendieck ring;Bilinear form;Bi-Frobenius algebra | Document URI: | http://hdl.handle.net/1942/30586 | ISSN: | 1386-923X | e-ISSN: | 1572-9079 | DOI: | 10.1007/s10468-018-9832-2 | ISI #: | WOS:000504321400011 | Rights: | Springer Nature B.V. 2018 | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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