Cohomology of dilute Temperley--Lieb algebras
Andrew Fisher, Daniel Graves
TL;DR
This paper proves that the cohomology of dilute Temperley--Lieb algebras is trivial in all positive degrees, providing new insights into their algebraic structure relevant to statistical mechanics.
Contribution
It establishes the vanishing of (co)homology in positive degrees for dilute Temperley--Lieb algebras, a key step in understanding their algebraic properties.
Findings
Cohomology vanishes in all positive degrees
Provides algebraic insights relevant to statistical mechanics
Advances understanding of dilute Temperley--Lieb algebras
Abstract
Dilute Temperley--Lieb algebras are variants of Temperley--Lieb algebras arising in statistical mechanics in the study of solvable lattice models. In this paper we prove that the (co)homology of dilute Temperley--Lieb algebras vanishes in all positive degrees.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra