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Search: All articles in the CMB digital archive with keyword homology

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26. CMB 2003 (vol 46 pp. 268)

Puls, Michael J.
Group Cohomology and $L^p$-Cohomology of Finitely Generated Groups
Let $G$ be a finitely generated, infinite group, let $p>1$, and let $L^p(G)$ denote the Banach space $\{ \sum_{x\in G} a_xx \mid \sum_{x\in G} |a_x |^p < \infty \}$. In this paper we will study the first cohomology group of $G$ with coefficients in $L^p(G)$, and the first reduced $L^p$-cohomology space of $G$. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.

Keywords:group cohomology, $L^p$-cohomology, central element of infinite order, harmonic function, continuous linear functional
Categories:43A15, 20F65, 20F18

27. CMB 2000 (vol 43 pp. 3)

Adin, Ron; Blanc, David
Resolutions of Associative and Lie Algebras
Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees.

Keywords:resolutions, homology, Lie algebras, associative algebras, non-associative algebras, Jacobi identity, leaf-labeled trees, associahedron
Categories:18G10, 05C05, 16S10, 17B01, 17A50, 18G50

28. CMB 1999 (vol 42 pp. 129)

Baker, Andrew
Hecke Operations and the Adams $E_2$-Term Based on Elliptic Cohomology
Hecke operators are used to investigate part of the $\E_2$-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of $\Ext^1$ which combines use of classical Hecke operators and $p$-adic Hecke operators due to Serre.

Keywords:Adams spectral sequence, elliptic cohomology, Hecke operators
Categories:55N20, 55N22, 55T15, 11F11, 11F25

29. CMB 1997 (vol 40 pp. 54)

Kechagias, Nondas E.
A note on $U_n\times U_m$ modular invariants
We consider the rings of invariants $R^G$, where $R$ is the symmetric algebra of a tensor product between two vector spaces over the field $F_p$ and $G=U_n\times U_m$. A polynomial algebra is constructed and these invariants provide Chern classes for the modular cohomology of $U_{n+m}$.

Keywords:Invariant theory, cohomology of the unipotent group
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