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Principal Components Along Quiver Representations
Foundations of Computational Mathematics, 2022 AbstractQuiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation of a finite quiver.
Anna Seigal +2 more
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Partition identities and quiver representations [PDF]
Journal of Algebraic Combinatorics, 2017 26 ...
Richard Rimányi +2 more
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On the Representation Ring of a Quiver
Algebras and Representation Theory, 2009The classical Clebsch-Gordan problem is to give a formula for decomposition of tensor product of two indecomposable representations of a group. In this paper a version of this problem is treated. Instead of representations of a group the representations of a quiver are considered and the tensor product is defined point-wise and arrow-wise. Fix a quiver
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General Representations of Quivers
Proceedings of the London Mathematical Society, 1992General representations of a quiver \(Q\) are investigated in the paper. Recall that the representations of a dimension vector \(\alpha\) of the quiver \(Q\) are parametrised by a vector space \(R(Q,\alpha)\) on which an algebraic group \(\text{Gl}(Q,\alpha)\) acts such that the orbits of the group on the space are in 1-1 correspondence with the ...
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Recovering Quivers from Derived Quiver Representations [PDF]
Communications in Algebra, 2013 We compute Balmer's prime spectrum for the derived category of quiver representations for a finite ordered quiver with the vertex-wise tensor product and show that it does not recover the quiver. We then associate an algebra to every k-linear triangulated tensor category and show that the path algebra can be recovered in this way.
Susan J Sierra
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REPRESENTATIONS OF QUIVERS OF INFINITE TYPE
Mathematics of the USSR-Izvestiya, 1973Summary: Translation from Izv. Akad. Nauk SSSR, Ser. Mat. 37, 752--791 (1973; Zbl 0298.15012).
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2018
A quiver is a finite directed graph. The associated path algebra has all paths of the quiver as a basis, and the multiplication is defined in terms of concatenating paths when possible. We have seen representations of a quiver earlier, and we also have seen how to relate representations of a quiver to modules for its path algebra.
Karin Erdmann, Thorsten Holm
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A quiver is a finite directed graph. The associated path algebra has all paths of the quiver as a basis, and the multiplication is defined in terms of concatenating paths when possible. We have seen representations of a quiver earlier, and we also have seen how to relate representations of a quiver to modules for its path algebra.
Karin Erdmann, Thorsten Holm
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2014
In this chapter, we introduce the concept of quiver representations and their morphisms, discuss direct sums, kernels, and cokernels, and study short exact sequences of quiver representations. We also introduce some basic notions of category theory.
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In this chapter, we introduce the concept of quiver representations and their morphisms, discuss direct sums, kernels, and cokernels, and study short exact sequences of quiver representations. We also introduce some basic notions of category theory.
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1982
This chapter introduces another aspect of the current research on representation of algebras. This Une of work began with the papers [34] and [35] of P. Gabriel. He gave an explicit construction of the indecomposable modules for certain finite dimensional F-algebras.
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This chapter introduces another aspect of the current research on representation of algebras. This Une of work began with the papers [34] and [35] of P. Gabriel. He gave an explicit construction of the indecomposable modules for certain finite dimensional F-algebras.
openaire +1 more source