## Missouri Journal of Mathematical Sciences

### Indicators of Pointed Hopf Algebras of Dimensions $pq$ Over Characteristic $p$

#### Abstract

Let $p$, $q$ be two distinct primes. We consider pointed Hopf algebras of dimension $pq$ over an algebraically closed field of characteristic $p$. We compute higher Frobenius-Schur indicators of these Hopf algebras through the associated graded Hopf algebras with respect to their coradical filtrations. The resulting indicators are gauge invariants for the monoidal representation categories of these algebras.

#### Article information

Source
Missouri J. Math. Sci., Volume 30, Issue 2 (2018), 176-184.

Dates
First available in Project Euclid: 7 December 2018

https://projecteuclid.org/euclid.mjms/1544151694

Mathematical Reviews number (MathSciNet)
MR3884739

#### Citation

Chen, Si; Liu, Tiantian; Wang, Linhong; Wang, Xingting. Indicators of Pointed Hopf Algebras of Dimensions $pq$ Over Characteristic $p$. Missouri J. Math. Sci. 30 (2018), no. 2, 176--184. https://projecteuclid.org/euclid.mjms/1544151694

#### References

• H. Hu, X. Hu, L. Wang, and X. Wang, Computing indicators of Radford algebras, Involve, A Journal of Mathematics, 11 (2018), 325–334.
• Y. Kashina, S. Montgomery, and S.-H. Ng, On the trace of the antipode and higher indicators, Israel J. Math., 188.1 (2012), 57–89.
• Y. Kashina, Y. Sommerhäuser, and Y. Zhu, On higher Frobenius-Schur indicators, Memories of the American Mathematical Society, 181.855 (2006), viii+65 pp.
• V. Linchenko and S. Montgomery, A Frobenius-Schur theorem for Hopf algebras, Algebr. Represent. Theory, 3.4 (2000), 347–355.
• S. Montgomery, Hopf algebras and their actions on rings, Vol. 82 of CBMS Regional Conference Series in Mathematics, published for the Conference Board of the Mathematical Sciences, Washington DC; by the American Mathematical Society, Providence, RI, 1993.
• K. Shimizu, On indicators of Hopf algebras, Israel J. Math., 207.1 (2015), 155–201.
• M. E. Sweedler, Hopf algebras, W. A. Benjamin, Inc., New York, 1969, Mathematics Lecture Note Series.
• R. Xiong, Pointed $p^2q$-dimensional Hopf algebras in positive characteristic, preprint, arXiv1705.00339.
• L. Wang and X. Wang, Indicators of Hopf algebras in positive characteristic, to appear in Arch. Math. (Basel).