Results 1 
6 of
6
The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra
, 2004
"... on the occasion of his sixtieth birthday Abstract. For a finite dimensional monomial algebra Λ over a field K we show that the Hochschild cohomology ring of Λ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated Kalgebra of Krull dimension at most one. Th ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
on the occasion of his sixtieth birthday Abstract. For a finite dimensional monomial algebra Λ over a field K we show that the Hochschild cohomology ring of Λ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated Kalgebra of Krull dimension at most one. This was conjectured to be true for any finite dimensional algebra over a field in [13].
CLUSTER FANS, STABILITY CONDITIONS, AND DOMAINS OF SEMIINVARIANTS
, 811
"... Abstract. We show that the cone of finite stability conditions of a quiver Q without oriented cycles has a fan covering given by (the dual of) the cluster fan of Q. Along the way, we give new proofs of Schofield’s results [17] on perpendicular categories. We also study domains of semiinvariants lab ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We show that the cone of finite stability conditions of a quiver Q without oriented cycles has a fan covering given by (the dual of) the cluster fan of Q. Along the way, we give new proofs of Schofield’s results [17] on perpendicular categories. We also study domains of semiinvariants labeled by real Schur roots via quiver exceptional sequences. In particular, we recover IgusaOrrTodorovWeyman’s theorem from [6] on cluster complexes and domains of semiinvariants for Dynkin quivers. 1.
A PARTIAL A∞STRUCTURE ON THE COHOMOLOGY OF
, 707
"... Abstract. Suppose k is a field of characteristic 2, and n, m ≥ 4 powers of 2. Then the A∞structure of the group cohomology algebras H ∗ (Cn, k) and H ∗ (Cm, k) are well known. We give results characterizing an A∞structure on H ∗ (Cn ×Cm, k) including limits on nonvanishing lowarity operations an ..."
Abstract
 Add to MetaCart
Abstract. Suppose k is a field of characteristic 2, and n, m ≥ 4 powers of 2. Then the A∞structure of the group cohomology algebras H ∗ (Cn, k) and H ∗ (Cm, k) are well known. We give results characterizing an A∞structure on H ∗ (Cn ×Cm, k) including limits on nonvanishing lowarity operations and an infinite family of nonvanishing higher operations. 1.
BLACKBOX COMPUTATION OF A∞ALGEBRAS
, 807
"... Abstract. Kadeishvili’s proof of the minimality theorem (Kadeishvili, T.; On the homology theory of fiber spaces, Russian Math. Surveys 35 (3) 1980) induces an algorithm for the inductive computation of an A∞algebra structure on the homology of a dgalgebra. In this paper, we prove that for one cla ..."
Abstract
 Add to MetaCart
Abstract. Kadeishvili’s proof of the minimality theorem (Kadeishvili, T.; On the homology theory of fiber spaces, Russian Math. Surveys 35 (3) 1980) induces an algorithm for the inductive computation of an A∞algebra structure on the homology of a dgalgebra. In this paper, we prove that for one class of dgalgebras, the resulting computation will generate a complete A∞algebra structure after a finite amount of computational work. Ainfinity, strong homotopy associativity, inductive computation 17A42; 1704 1.
CLUSTER FANS, STABILITY CONDITIONS, AND DOMAINS OF
, 811
"... ABSTRACT. We show that the cone of finite stability conditions of a quiver Q without oriented cycles has a fan covering given by (the dual of) the cluster fan of Q. Along the way, we give new proofs of Schofield’s results [18] on perpendicular categories. From our results, we recover IgusaOrrTodor ..."
Abstract
 Add to MetaCart
ABSTRACT. We show that the cone of finite stability conditions of a quiver Q without oriented cycles has a fan covering given by (the dual of) the cluster fan of Q. Along the way, we give new proofs of Schofield’s results [18] on perpendicular categories. From our results, we recover IgusaOrrTodorovWeyman’s theorem from [7] on cluster complexes and domains of semiinvariants for Dynkin quivers. For arbitrary quivers, we also give a description of the domains of semiinvariants labeled by real Schur roots in terms of quiver exceptional sets. 1.