Related papers: Generalization of the Correspondence about DTr-sel…

We prove that the representation dimension of a selfinjective algebra of wild tilted type is equal to three, and give an explicit construction of an Auslander generator of its module category. We also show that if a connected selfinjective…

We prove that the representation dimension of a selfinjective algebra of euclidean type is equal to three, and give an explicit construction of the Auslander generator of its module category.

For every $n \geq 1$, we present examples of algebras $A$ having dominant dimension $n$, such that the algebra $B=End_A(I_0 \oplus \Omega^{-n}(A))$ has dominant dimension different from $n$, where $I_0$ is the injective hull of $A$. This…

For a positively graded artin algebra $A=\oplus_{n\geq 0}A_n$ we introduce its Beilinson algebra $\mathrm{b}(A)$. We prove that if $A$ is well-graded self-injective, then the category of graded $A$-modules is equivalent to the category of…

For a prime p and natural number n with p greater than or equal to n, we establish the existence of a non-functorial one-to-one correspondence between isomorphism classes of groups of order p^n whose derived subgroup has exponent dividing…

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is…

Derived equivalences between finite dimensional algebras do, in general, not pass to centraliser (or other) subalgebras, nor do they preserve homological invariants of the algebras, such as global or dominant dimension. We show that,…

We investigate the behavior of the homological dimensions under recollements of derived categories of algebras. In particular, we establish a series of new bounds among the selfinjective dimension or $\phi$-dimension of the algebras linked…

A description of the Ziegler spectrum is given for trivial extensions of tubular algebras and related self-injective algebras of tubular type.

In this work $n$-dimensional filiform Leibniz algebras admitting a gradation of length $(n-1)$ are classified. Derivations of such algebras are also described.

We establish a bijective correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures of $\mathsf{D}_{\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more…

For monomial special multiserial algebras, which in general are of wild representation type, we construct radical embeddings into algebras of finite representation type. As a consequence, we show that the representation dimension of…

We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…

We describe the structure of finite dimensional selfinjective algebras over an arbitrary field without short cycles of indecomposable modules.

The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categories, we study dominant dimensions of algebras under derived…

We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.

We consider endomorphism algebras of $n$-term silting complexes in derived categories of hereditary algebras, and we show that the module category of such an endomorphism algebra has a separated $n$-section. For $n=3$ we obtain a trisection…

We provide a complete classification of finite-dimensional self-injective algebras which are socle equivalent to preprojective algebras of generalized Dynkin type. In particular, we conclude that these algebras are deformed preprojective…

The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective finite dimensional algebra is finite. In \cite{Yam}, Yamagata stated the stronger conjecture that the dominant dimension of a non-selfinjective finite…

In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra,…