Grothendieck Groups of a Class of Quantum Doubles
Grothendieck Groups of a Class of Quantum Doubles
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DOI：
10.1142/s1005386708000412
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发表时间：
2008-09
影响因子：
0.3
通讯作者：
Yun Zhang;Feng Wu;Lingzhen Liu;Hui-xiang Chen
中科院分区：
文献类型：
--
作者：
Yun Zhang;Feng Wu;Lingzhen Liu;Hui-xiang Chen
Let k be a field and An(ω) be the Taft n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. We have constructed an n4-dimensional Hopf algebra Hn(p,q) which is isomorphic to D(An(ω)) if p ≠ 0 and q = ω-1, and studied the irreducible and finite-dimensional representations of Hn(1,q). In this paper, we continue our study of Hn(1,q), examine the Grothendieck group G0(Hn(1,q)) ≅ G0(D(An(ω)), and describe its ring structure. We also give the Loewy length of the tensor product of two simple modules over Hn(1,q).
