Search arXiv⌕ Search

arXiv · 0705.1152

The cyclic homology of monogenic extensions in the noncommutative setting

Abstract

We study the Hochschild and cyclic homologies of noncommutative monogenic extensions. As an aplication we compute the Hochschild and cyclic homologies of the rank~1 Hopf algebras introduced by L. Krop and D. Radford in [Finite dimensional Hopf algebras of rank 1 in characteristic 0, Journal of Algebra 302, no. 1, 214-230} (2006)].

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Graciela Carboni, Jorge A. Guccione, Juan J. Guccione. 2007-05-08. The cyclic homology of monogenic extensions in the noncommutative setting. https://arxiv.org/abs/0705.1152

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

The K-theory of left pointed derivators

We build on work of Muro-Raptis in [Ann. K-Theory 2 (2017), no. 2, 303-340] and Cisinski-Neeman in [Adv. Math. 217 (2008), no. 4, 1381-1475] to prove that the additivity of derivator K-theory holds for a large class of derivators that we call left pointed derivators, which includes all triangulated derivators. The proof methodology is an adaptation of the combinatorial methods of Grayson in [Doc. Math. 16 (2011), 457-464]. As a corollary, we prove that derivator K-theory is an infinite loop space. Finally, we speculate on the role of derivator K-theory as a trace from the algebraic K-theory of a stable $\infty$-category à la Blumberg-Gepner-Tabuada in [Geom. Topol. 17 (2013), no. 2, 733-838].

math.KT↗

Solving the index problem for (curved) Bernstein-Gelfand-Gelfand sequences

We study the index theory of curved Bernstein-Gelfand-Gelfand (BGG) sequences in parabolic geometry and their role in $K$-homology and noncommutative geometry. The BGG-sequences fit into $K$-homology, and we solve their index problem. We provide a condition for when the BGG-complex on the flat parabolic geometry $G/P$ of a semisimple Lie group $G$ fits into $G$-equivariant $K$-homology by means of Heisenberg calculus. For higher rank Lie groups, we prove a no-go theorem showing that the approach fails.

math.KT↗

Roe algebras and coarse index maps for spaces with proper actions of {é}tale groupoids. I

This is the first in a series of papers extending Roe algebras and coarse index theory to the groupoid-equivariant setting. We introduce some techniques to develop a framework of Roe algebras and their K-theory for spaces equipped with proper actions of {é}tale groupoids. For a fixed {é}tale groupoid G and G-C* -algebra A, we construct a functor KC(-; G, A) from the category of locally compact Hausdorff proper G-spaces and equivariant proper continuous maps to the category of graded abelian groups, which provides a natural receptacle for an equivariant coarse index map. We study the existence of universal modules, an analog of ample modules in non-equivariant setting, and develop a decomposition technique to establish their existence. As an application, we prove that groupoid simplicial complexes satisfying suitable hypotheses admit universal modules.

math.KT↗