Computing the Frobenius–Schur Indicator for Abelian Extensions of Hopf Algebras

✍ Scribed by Y. Kashina; G. Mason; S. Montgomery

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 201 KB
• Volume: 251
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.9129

✦ Synopsis

2 × 2 . If H is abelian of order 8, we may use K = k H * , and if H is abelian of order 4 we use K = kD 8 * . If H ∼ = D 8 , then in the two possible examples, one has K = kD 8

* and the other has K = kQ 8 * . If H ∼ = 2 × 2 × 2 then H has two simple degree 2 characters, χ 1 and χ 2 , and they are self-dual (see [K, Sect. 3.2]). Therefore by Lemma 7.1, ν χ 1 = ν χ 2 = 1.