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Configurations of trivial extensions of Dynkin type An
(Academic Press Inc Elsevier Science, 2004-11)
Let Λ be a trivial extension of Cartan class An. We find a combinatorial algorithm giving the configurations of ℤAn associated to Λ.
ON THE REPRESENTATION TYPE OF CERTAIN TRIVIAL EXTENSIONS
(Universidad Católica del Norte, Departamento de Matemáticas, 2001)
Cohomology of split algebras and of trivial extensions
(Cambridge University Press, 2003-01)
We consider associative algebras λ over a field provided with a direct sum decomposition of a two-sided ideal M and a sub-algebra A - examples are provided by trivial extensions or triangular type matrix algebras. In this ...
The first cohomology group of the trivial extension of a monomial algebra
(World Scientific, 2004-12)
Given a finite-dimensional monomial algebra A, we consider the trivial extension TA and provide formulae, depending on the characteristic of the field, for the dimensions of the summands HH1(A) and Alt(DA) of the first ...
On m-cluster tilted algebras and trivial extensions
(Academic Press Inc Elsevier Science, 2013-01)
In this work we study the connection between iterated tilted algebras and m-cluster tilted algebras. We show that an iterated tilted algebra induces an m-cluster tilted algebra. This m-cluster tilted algebra can be seen ...
On the representation dimension of some classes of algebras
(Academic Press Inc Elsevier Science, 2004-05)
We show that the representation dimension of the following classes of algebras is at most 3: (a) Artin algebras A such that the functor HomA (D(A), -) has finite length (or dually, HomA (-, A) has finite length). These ...
On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras
(Academic Press Inc Elsevier Science, 2020-09)
In this paper we determine the first Hochschild homology and cohomology with different coefficients for gentle algebras and we give a geometrical interpretation of these (co)homologies using the ribbon graph of a gentle ...
Trivial central extensions of Lie bialgebras
(Academic Press Inc Elsevier Science, 2013-09)
From a Lie algebra g satisfying Z(g)=0 and Λ2(g)g=0 (in particular, for g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form L=g×K{double-struck} in terms of Lie bialgebra structures ...