Triangular decomposition of $\mathrm{SL}_3$ skein algebras

Biflatness and Biprojectivitiy of Triangular Banach Algebras

Skein Theory for the D2n Planar Algebras

Abstract We give a combinatorial description of the “D2n planar algebra”, by giving generators and relations. This includes a direct proof that the relations are consistent, as well as a complete description of the associated tensor category and its principal graph. While we use the usual langauge of subfactor planar algebras, the entire argument is ‘skein-theoretic’, and there is no functional...

Skein theory for the ADE planar algebras

We give generators and relations for the planar algebras corresponding to the E8 subfactor. We also give an explicit basis, and an algorithm to express an arbitrary diagram as a linear combination of basis diagrams. We summarize the analogous results for the other ADE subfactors, which can be obtained by the same methods. © 2009 Elsevier B.V. All rights reserved.

Positive basis for surface skein algebras.

We show that the twisted SL2 skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.

Triangular Algebras and Ideals of Nest Algebras

Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...