• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.701-718
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• 2019

In this paper we compute the U-projective resolution of kQ-modules where Q is quiver of type $A_n$ and ${\tilde{A}}_n$. The behavior of the sequence can be seen through its geometric representation.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.213-222
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• 2021

In this paper we investigate the Baer-Kaplansky theorem for module classes on algebras of finite representation types over a field. To do this we construct finite dimensional quiver algebras over any field.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1177-1187
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• 2014

In the current paper we study absolutely pure representations of quivers. Then over some nice quivers including linear quivers some sufficient conditions guaranteeing a representation to be absolutely pure is characterized. Furthermore some relations between atness and absolute purity is investigated. Finally it is shown that the absolutely pure covering of representations of linear quivers (including $A^-_{\infty}$, $A^+_{\infty}$ and $A^{\infty}_{\infty}$) by R-modules whenever R is a coherent ring exists.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.353-385
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• 2019

In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers for commutation classes [${\tilde{w}}]$ of w in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order ${\prec}_{[{\tilde{w}}]}$ on the subset ${\Phi}(w)$ of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection functors, we can apply their properties to the representation theory of KLR algebras and dual PBW-basis associated to any commutation class [${\tilde{w}}_0$] of the longest element $w_0$ of any finite type.