A note on a paper by Cuadra, Etingof and Walton. (English) Zbl 1369.16032
Summary: We analyze the proof of the main result of a paper by J. Cuadra et al. [Adv. Math. 282, 47–55 (2015; Zbl 1369.16026)], which says that any action of a semisimple Hopf algebra \(H\) on the \(n\)th Weyl algebra \(A=A_n(K)\) over a field \(K\) of characteristic \(0\) factors through a group algebra. We verify that their methods can be used to show that any action of a semisimple Hopf algebra \(H\) on an iterated Ore extension of derivation type \(A=K[x_1;d_1][x_2;d_2][\cdots][x_n;d_n]\) in characteristic zero factors through a group algebra.
MSC:
16T05 | Hopf algebras and their applications |
13A35 | Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure |
Citations:
Zbl 1369.16026References:
[1] | Atiyah M. F., Introduction to Commutative Algebra. Reading, MA/London/Don (1969) · Zbl 0175.03601 |
[2] | DOI: 10.1016/j.jalgebra.2013.09.002 · Zbl 1306.16026 · doi:10.1016/j.jalgebra.2013.09.002 |
[3] | DOI: 10.1016/j.aim.2015.05.014 · Zbl 1369.16026 · doi:10.1016/j.aim.2015.05.014 |
[4] | DOI: 10.1016/j.aim.2013.10.008 · Zbl 1297.16029 · doi:10.1016/j.aim.2013.10.008 |
[5] | DOI: 10.1007/BF01179855 · Zbl 0042.26401 · doi:10.1007/BF01179855 |
[6] | DOI: 10.2307/2372000 · Zbl 0046.03402 · doi:10.2307/2372000 |
[7] | Kadison L., Algebra and its Applications (2000) · Zbl 1267.81211 |
[8] | DOI: 10.1007/BF01238035 · Zbl 0043.03802 · doi:10.1007/BF01238035 |
[9] | DOI: 10.1081/AGB-200036837 · Zbl 1078.16044 · doi:10.1081/AGB-200036837 |
[10] | Radford D. E., Hopf Algebras (2012) |
[11] | DOI: 10.1016/j.jalgebra.2006.06.030 · Zbl 1109.16033 · doi:10.1016/j.jalgebra.2006.06.030 |
[12] | Strade H., Modular Lie Algebras and their Representations (1988) · Zbl 0648.17003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.