Open Frobenius Cluster-Tilted Algebras

In this paper, we compute the Frobenius dimension of any cluster-tilted algebra of finite type. Moreover, we give conditions on the bound quiver of a cluster-tilted algebra [Formula: see text] such that [Formula: see text] has non-trivial open Frobenius structures.

On the multifractal spectrum of weighted Birkhoff averages

<p style='text-indent:20px;'>In this paper, we study the topological spectrum of weighted Birk–hoff averages over aperiodic and irreducible subshifts of finite type. We show that for a uniformly continuous family of potentials, the spectrum is continuous and concave over its domain. In case of typical weights with respect to some ergodic quasi-Bernoulli measure, we determine the spectrum. Moreover, in case of full shift and under the assumption that the potentials depend only on the first coordinate, we show that our result is applicable for regular weights, like Möbius sequence.</p>

Equivariant connective 𝐾-theory

For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective K K -theory mapping to the equivariant K K -homology of Guillot and the equivariant algebraic K K -theory of Thomason. It has all the standard basic properties as the homotopy invariance and localization. We also get the equivariant version of the Brown-Gersten-Quillen spectral sequence and study its convergence.