Let p be a prime number, k an algebraically closed field of characteristic p, G˜ a finite group,
and G a normal subgroup of G˜ having ap-power index in G˜. Moreover let B be a block of kG …

Derived categories and equivalences between them are the pièce de résistance of modern
homological algebra. They are widely used in many branches of mathematics, especially in …

This thesis is based on [6] and [7]. In this thesis, we investigate two-sided tilting complexes
for Brauer tree algebras. Throughout this thesis let A be a Brauer tree algebra over an …

In this paper we construct non-negative gradings on a basic Brauer tree algebra AΓ
corresponding to an arbitrary Brauer tree Γ of type (m, e). We do this by transferring gradings …

According to a result claimed by Pogorza_ly, selfinjective special biserial algebras can be
stably equivalent to stably biserial algebras only, and these two classes coincide. By an …

In this note, for a Brauer tree algebra A and a star-shaped Brauer tree algebra B which is
derived equivalent to A, we give operations on the two-sided tilting complex D_T of A⊗B^op …

By a result claimed by Pogorza\l {} y selfinjective special biserial algebras can be stably
equivalent only to stably biserial algebras and these two classes coincide. By an example of …

arXiv:1009.3210v3 [math.RA] 7 Jul 2011 Page 1 arXiv:1009.3210v3 [math.RA] 7 Jul 2011
MUTATING BRAUER TREES TAKUMA AIHARA Abstract. In this paper we introduce mutation of …

We study the relation between simple-minded systems and two-term tilting complexes for
self-injective Nakayama algebras. More precisely, we show that any simple-minded system …

Deformations, Tiltings, and Decomposition Matrices Page 1 Fields Institute Communications
Volume 00, 0000 Deformations, Tiltings, and Decomposition Matrices Mary Schaps …