Triangular matrix coalgebras and applications
MC Iovanov - Linear and Multilinear Algebra, 2015 - Taylor & Francis
We formally introduce and study generalized comatrix coalgebras and upper triangular
comatrix coalgebras, which are not only a dualization but also an extension of classical …
comatrix coalgebras, which are not only a dualization but also an extension of classical …
When does the rational torsion split off for finitely generated modules
MC Iovanov - Algebras and representation theory, 2009 - Springer
It is well known that the torsion part of any finitely generated module over the formal power
series ring K [[X]] is a direct summand. In fact, K [[X]] is an algebra dual to the divided power …
series ring K [[X]] is a direct summand. In fact, K [[X]] is an algebra dual to the divided power …
[HTML][HTML] Infinite dimensional serial algebras and their representations
MC Iovanov - Journal of algebra, 2018 - Elsevier
We study arbitrary algebras all of whose indecomposable finite dimensional representations
are uniserial, or more generally, comodules over serial coalgebras. We show that the infinite …
are uniserial, or more generally, comodules over serial coalgebras. We show that the infinite …
On extensions of rational modules
MC Iovanov - Israel Journal of Mathematics, 2014 - Springer
Given a topological algebra A, we investigate when the categories of all rational A-modules
and of finite-dimensional rational modules are closed under extensions inside the category …
and of finite-dimensional rational modules are closed under extensions inside the category …
[PDF][PDF] Serial categories, quantum groups and the pure semisimplicity conjecture
M Iovanov - Preprint-posted online by author - homepage.divms.uiowa.edu
We consider the pure semisimplicity conjecture in the infinite dimensional case: if in the
category A-lf of locally finite left A-modules over an algebra A every object decomposes as a …
category A-lf of locally finite left A-modules over an algebra A every object decomposes as a …
On the infinite tame-wild dichotomy conjecture and related problemns
MC Iovanov - arXiv preprint arXiv:1803.00173, 2018 - arxiv.org
We prove the tame-wild dichotomy conjecture, due to D. Simson, for infinite dimensional
algebras and coalgebras. The key part of the approach is proving new representation …
algebras and coalgebras. The key part of the approach is proving new representation …
Symmetry for comodule categories
S Crivei, MC Iovanov - Journal of Algebra and Its Applications, 2012 - World Scientific
For coalgebras C over a field, we study when the categories of left C-comodules and of right
C-comodules are symmetric categories, in the sense that there is a duality between the …
C-comodules are symmetric categories, in the sense that there is a duality between the …
The representation theory of profinite algebras: Interactions with category theory, algebraic topology and compact groups
MC Iovanov - 2009 - search.proquest.com
In the present text, we examine current trends in the theory of profinite algebras, and
applications, connections and interactions with other fields of mathematics. The thesis …
applications, connections and interactions with other fields of mathematics. The thesis …
The finite Rat-splitting for coalgebras
MC Iovanov - arXiv preprint math/0612478, 2006 - arxiv.org
Let $ C $ be a coalgebra. We investigate the problem of when the rational part of every
finitely generated $ C^* $-module $ M $ is a direct summand $ M $. We show that such a …
finitely generated $ C^* $-module $ M $ is a direct summand $ M $. We show that such a …
[PDF][PDF] THE INFINITE TAME-WILD DICHOTOMY AND BRAUER-THRALL 3 CONJECTURES
MC IOVANOV - arXiv preprint arXiv:1803.00173, 2018 - researchgate.net
We prove the tame-wild dichotomy conjecture, due to D. Simson, for infinite dimensional
algebras and coalgebras. The key part of the approach is proving new representation …
algebras and coalgebras. The key part of the approach is proving new representation …