O-Species and SPSD-Rings of Bounded Representation Type

2016 ◽  
pp. 255-296
Keyword(s):  
Representation Type ◽  
Bounded Representation

A Note on the Representation Type of Pointed Irreducible Coalgebras and Unipotent Algebras

1977 ◽  
Vol 29 (1) ◽  
pp. 220-223
Author(s):  
David Trushin
Keyword(s):  
Finite Sequence ◽  
Representation Type ◽  
Finite Dimensional ◽  
Bounded Representation ◽  
Divided Powers

In this paper the representation type of the class of pointed irreducible coalgebras is studied. We refer the reader to [4] for the basic definitions. A coalgebra is of bounded representation type if there is a bound on the dimension of finite dimensional indecomposable comodules. In Section 1, we show that the representation type is dependent upon the size of the space of primitives. Indeed, a pointed irreducible coalgebra is of bounded type if and only if it is finite dimensional and the space of primitives is onedimensional, i.e. if and only if it is a coalgebra spanned by a finite sequence of divided powers.

scholarly journals The class of(1,3)-groups with homocyclic regulator quotient of exponentp4has bounded representation type

2014 ◽  
Vol 400 ◽  
pp. 43-55 ◽  
Author(s):  
David M. Arnold ◽  
Adolf Mader ◽  
Otto Mutzbauer ◽  
Ebru Solak
Keyword(s):  
Representation Type ◽  
Bounded Representation

THE CLASS OF (2, 2)-GROUPS WITH HOMOCYCLIC REGULATOR QUOTIENT OF EXPONENT  HAS BOUNDED REPRESENTATION TYPE

2014 ◽  
Vol 99 (1) ◽  
pp. 12-29
Author(s):  
DAVID M. ARNOLD ◽  
ADOLF MADER ◽  
OTTO MUTZBAUER ◽  
EBRU SOLAK
Keyword(s):  
Representation Type ◽  
Bounded Representation ◽  
Decomposable Groups

The class of almost completely decomposable groups with a critical typeset of type$(2,2)$and a homocyclic regulator quotient of exponent $p^{3}$is shown to be of bounded representation type. There are only$16$isomorphism at$p$types of indecomposables, all of rank $8$or lower.

The Representation Type of Algebras and Subalgebras

1958 ◽  
Vol 10 ◽  
pp. 39-44 ◽  
Author(s):  
J. P. Jans
Keyword(s):  
Associative Algebra ◽  
Representation Type ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Bounded Representation

For A an associative algebra with identity over a field K, [A : K] < ∞, and d an integer, we define g Λ(d) to be the number of inequivalent indecomposable Λ-modules of degree d over K. Following (6), we define Λ to be of finite representation type if . Λis said to be of bounded representation type if there exists d 0 such that g Λ(d) = 0 for d ⩾ d 0; Λ is of unbounded representation type if not of bounded type.

scholarly journals Algebras of bounded finite dimensional representation type

1995 ◽  
Vol 37 (3) ◽  
pp. 289-302 ◽  
Author(s):  
Allen D. Bell ◽  
K. R. Goodearl
Keyword(s):  
Representation Type ◽  
Dimensional Representation ◽  
Dimensional Algebra ◽  
Finite Dimensional Representation ◽  
Finite Representation ◽  
Finite Representation Type ◽  
Finite Dimensional ◽  
Left And Right ◽  
Bounded Representation ◽  
Algebra Over A Field

It is well known that for finite dimensional algebras, “bounded representation type” implies “finite representation type”; this is the assertion of the First Brauer-Thrall Conjecture (hereafter referred to as Brauer-Thrall I), proved by Roiter [26] (see also [23]). More precisely, it states that if R is a finite dimensional algebra over a field k, such that there is a finite upper bound on the k-dimensions of the finite dimensional indecomposable right R-modules, then up to isomorphism R has only finitely many (finite dimensional) indecomposable right modules. The hypothesis and conclusion are of course left-right symmetric in this situation, because of the duality between finite dimensional left and right R-modules, given by Homk(−, k). Furthermore, it follows from finite representation type that all indecomposable R modules are finite dimensional [25].

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