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2 results

Skew Derivations in Banach Algebras
Pao-Kuei Liau, Cheng-Kai Liu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 3 / October 2015

Published online by Cambridge University Press:

10 June 2015, pp. 683-696
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We investigate the global versions of the Kleinecke–Shirokov theorem for skew derivations in Banach algebras. Centralizing skew derivations on Banach algebras are also studied.

Affine Actions of Uq(sl(2)) on Polynomial Rings
Jeffrey Bergen
Journal:

Canadian Mathematical Bulletin / Volume 58 / Issue 2 / 01 June 2015

Published online by Cambridge University Press:

20 November 2018, pp. 233-240

Print publication:

01 June 2015
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We classify the affine actions of ${{U}_{q}}\left( sl\left( 2 \right) \right)$ on commutative polynomial rings in $m\,\ge \,1$ variables. We show that, up to scalar multiplication, there are two possible actions. In addition, for each action, the subring of invariants is a polynomial ring in either $m$ or $m\,-\,1$ variables, depending upon whether $q$ is or is not a root of 1.