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Superpotentials and Quiver Algebras for Semisimple Hopf Actions
We consider the action of a semisimple Hopf algebra H on an m -Koszul Artin–Schelter regular algebra A . Such an algebra A is a derivation-quotient...
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Representations of Quivers over Artinian Rings
Given a unitary artinian ring R and a finite acyclic quiver Q , let Λ := R Q be the path ring of Q over R . Then Gorenstein-projective Λ -modules are...
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Finite-dimensional Algebras are (m> 2)-Calabi-Yau-tilted
We observe that over an algebraically closed field, any finite-dimensional algebra is the endomorphism algebra of an m -cluster-tilting object in a...
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Counting the Number of τ-Exceptional Sequences over Nakayama Algebras
The notion of a τ -exceptional sequence was introduced by Buan and Marsh in (
2018 ) as a generalisation of an exceptional sequence for finite... -
Organising the module category
We describe here the work developed with my students along the years in the IME-USP.
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A Simple Homological Characterization of String Algebras of Finite Representation Type
We prove that among the finite-dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the...
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Homological dimensions of gentle algebras via geometric models
Let A = kQ/I be a finite-dimensional basic algebra over an algebraically closed field k which is a gentle algebra with the marked ribbon surface
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Gröbner–Shirshov Basis of Derived Hall Algebra of Type An
We know that in Ringel-Hall algebra of Dynkin type, the set of all skew commutator relations between the iso-classes of indecomposable modules forms...
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Σ -Functions of the Categories of Matrix Representations of Nilpotent Semigroups
We study the categories of matrix representations of nilpotent semigroups over an arbitrary field. Our main attention is given to the Auslander...
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Further Comments
In this chapter we collect some comments on dichotomy problems in more general base fields, and some pertinent historical remarks.
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Simply Connected Algebras
In this chapter we study a family of tame algebras known as weakly separating family of coils. We introduce their basic properties and propose a...
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On the Braid Group Action on Exceptional Sequences for Weighted Projective Lines
We give a new and intrinsic proof of the transitivity of the braid group action on the set of full exceptional sequences of coherent sheaves on a...
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Group Actions on Algebras and Module Categories
In this chapter we study universal coverings of algebras and their counterpart, smash products. We deal with algorithmic constructions based on the...