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Hochschild cohomology of tensor products of topological algebras
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 2 / June 2010
- Published online by Cambridge University Press:
- 30 April 2010, pp. 447-470
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We describe explicitly the continuous Hochschild and cyclic cohomology groups of certain tensor products of
-algebras which are Fréchet spaces or nuclear DF-spaces. To this end we establish the existence of topological isomorphisms in the Künneth formula for the cohomology of complete nuclear DF-complexes and in the Künneth formula for continuous Hochschild cohomology of nuclear -algebras which are Fréchet spaces or DF-spaces for which all boundary maps of the standard homology complexes have closed ranges.
-algebras which are Fréchet spaces or nuclear A Künneth Theorem for p-Adic Groups
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- Journal:
- Canadian Mathematical Bulletin / Volume 50 / Issue 3 / 01 September 2007
- Published online by Cambridge University Press:
- 20 November 2018, pp. 440-446
- Print publication:
- 01 September 2007
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Let
${{G}_{1}}$ and 
${{G}_{2}}$ be 
$p$-adic groups. We describe a decomposition of Ext-groups in the category of smooth representations of 
${{G}_{1}}\times {{G}_{2}}$ in terms of Ext-groups for ${{G}_{1}}$ and ${{G}_{2}}$. We comment on 
$\text{Ext}_{G}^{1}\left( \pi ,\pi \right)$ for a supercuspidal representation 
$\pi$ of a $p$-adic group 
$G$. We also consider an example of identifying the class, in a suitable 
$E\text{x}{{\text{t}}^{1}}$, of a Jacquet module of certain representations of $p$-adic 
$\text{G}{{\text{L}}_{2n}}$.
