τ\tau-tilting finiteness of two-point algebras I

In this paper, we give criteria on $\tau$-tilting finiteness for two kinds of two-point algebras. Moreover, we show the $\tau$-tilting finiteness of some algebras, such as the (infinite-)tame block algebras of Hecke algebras of classical type over an algebraically closed field of characteristic not equal to 2, and the algebras from Table T and Table W introduced by Han [19].Comment: 25 page

A seminormal form for partition algebras

Using a new presentation for partition algebras (J. Algebraic Combin. 37(3):401-454, 2013), we derive explicit combinatorial formulae for the seminormal representations of the partition algebras. These results generalise to the partition algebras the classical formulae given by Young for the symmetric group.Comment: Published version. 51 pages, includes figures and table

Algebras from surfaces without punctures

We introduce a new class of finite dimensional gentle algebras, the surface algebras, which are constructed from an unpunctured Riemann surface with boundary and marked points by introducing cuts in internal triangles of an arbitrary triangulation of the surface. We show that surface algebras are endomorphism algebras of partial cluster-tilting objects in generalized cluster categories, we compute the invariant of Avella-Alaminos and Geiss for surface algebras and we provide a geometric model for the module category of surface algebras.Comment: 34 pages, 16 figures, 1 table, v2 reference adde

Determination of division algebras with 243 elements

Finite nonassociative division algebras (i.e., finite semifields) with 243 elements are completely classified.Comment: 6 pages, 3 table