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Growth of k-Dimensional Systoles in Congruence Coverings
We study growth of absolute and homological k -dimensional systoles of arithmetic n -manifolds along congruence coverings. Our main interest is in the...
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A symmetric approach to higher coverings in categorical Galois theory
In the context of a tower of (strongly Birkhoff) Galois structures in the sense of categorical Galois theory, we show that the concept of a higher...
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Representations of Algebras Tame and Wild Behavior
This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many...
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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...
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Torsion Theories and Coverings of V-Groups
For a commutative, unital and integral quantale V , we generalize to V -groups the results developed by Gran and Michel for preordered groups. We first...
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Higher Coverings of Racks and Quandles—Part II
This article is the second part of a series of three articles, in which we develop a higher covering theory of racks and quandles. This project is...
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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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Torsion theories and coverings of preordered groups
We explore a non-abelian torsion theory in the category of preordered groups: the objects of its torsion-free subcategory are the partially ordered...
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On Connected Components of Skew Group Algebras
Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group. There is a quiver Q G ...
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Homomorphisms and Coverings
The results about Lie subgroups proved so far allow to obtain information about homomorphisms between Lie groups. The idea is that the graph of a...
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On the Gleason-Kahane-Żelazko Theorem for Associative Algebras
The classical Gleason-Kahane-Żelazko Theorem states that a linear functional on a complex Banach algebra not vanishing on units, and such that
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Simple Modules for Kumjian-Pask Algebras
The paper introduces the notion of a representation k -graph (Δ, α ) for a given k -graph Λ. It is shown that any representation k -graph for Λ yields a...
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On factorizations of generically etale double coverings
A genus theory for double coverings or, equivalently, quadratic algebras is presented extending well-known concepts from number theory to geometry.
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On Wild Algebras and Super-Decomposable Pure-Injective Modules
Assume that k is an algebraically closed field and A is a finite-dimensional wild k -algebra. Recently, L. Gregory and M. Prest proved that in this...
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Lie Groups and Lie Algebras
This chapter conveys the basic principles governing the theory of Lie groups. A Lie group is a combination of three simultaneously different...
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Infinite-dimensional (dg) Lie algebras and factorization algebras in algebraic geometry
Infinite-dimensional Lie algebras (such as Kac-Moody, Virasoro etc.) govern, in many ways, various moduli spaces associated to algebraic curves. To...
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Representation Type of Borel-Schur Algebras
In our previous work (Erdmann et al. J. Algebra Appl. 17(2),1850028,
2018 ), we found all Borel-Schur algebras of finite representation type. In the...