Invertibility of elements in the ‎p‎ath algebra of a quiver

Document Type : Research Paper

Authors

Department of‎‎ Mathematics,‎‎ University of Calicut, St‎. ‎Thomas College‎, ‎‎‎Thrissur‎, ‎India

Abstract

‎The current study elucidates the nature of right and left inverses of an element in the path algebra of a quiver‎. ‎A general characterisation‎ ‎of such elements has been established‎. ‎An explicit formula to calculate the‎ ‎inverse element has been formulated‎. ‎It is observed that the left and right‎ ‎inverses of an element in the non-commutative path algebraic structure coincides‎. ‎Furthermore‎, ‎it is noted that the Jacobson radical of any finite dimensional path algebra can be easily found using this characterisation‎.

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References

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[5] M. Viji and R. S. Chakravarti, (2012). On quivers and incidence algebra, Glob. J. Sci. Front. Res., 12 (2012).

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