Communication and identification

Shipman, Mary; Bolam, David N.; Jenkins, Daniel

doi:10.4324/9780429454004-2

Cited by 1 publication

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“…The following consequence, addressing the relative sizes of the closures Rep S, is now immediate. It was independently obtained by I. Shipman with different methods; he also developed an algorithm for checking the considered inclusion via matrices of dimension vectors [23]. Algorithmic counterparts to the upcoming Corollary 4.4 and Theorem 4.5 will be addressed in 5.B.…”

Section: The Main Results For Truncated λmentioning

confidence: 99%

Closures in varieties of representations and irreducible components

Goodearl

Huisgen-Zimmermann

2018

Alg. Number Th.

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For any truncated path algebra Λ of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties Rep d (Λ) of the Λ-modules with fixed dimension vector d. In this situation, the components of Rep d (Λ) are always among the closures Rep S, where S traces the semisimple sequences with dimension vector d, and hence the key to the classification problem lies in a characterization of these closures.Our first result concerning closures actually addresses arbitrary basic finite dimensional algebras over an algebraically closed field. In the general case, it corners the closures Rep S by means of module filtrations "governed by S"; in case Λ is truncated, it pins down the Rep S completely.The analysis of the varieties Rep S leads to a novel upper semicontinuous module invariant which provides an effective tool towards the detection of components of Rep d (Λ) in general. It detects all components when Λ is truncated.

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Section: The Main Results For Truncated λmentioning

confidence: 99%