Kyu-Hwan Lee

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In this paper, we develop the Gr6bner-Shirshov basis theory for the representations of associative algebras by introducing the notion of Gr6bner-Shirshov pairs. Our result can be applied to solve the reduction problem in representation theory and to construct monomial bases of representations of associative algebras. As an illustration, we give an explicit(More)
We construct a new efficient algorithm for finding Gröbner–Shirshov bases for noncommutative algebras and their representations. This algorithm uses the Macaulay matrix [F.S. Macaulay, On some formula in elimination, Proc. London Math. Soc. 33 (1) (1902) 3–27], and can be viewed as a representation theoretic analogue of the F4 algorithm developed by J.C.(More)
We show that a set of monic polynomials in the free Lie superalgebra is a Gröbner-Shirshov basis for a Lie superalgebra if and only if it is a Gröbner-Shirshov basis for its universal enveloping algebra. We investigate the structure of GröbnerShirshov bases for Kac-Moody superalgebras and give explicit constructions of Gröbner-Shirshov bases for classical(More)
We report the production of a two-dimensional (2D) heterostructured gas sensor. The gas-sensing characteristics of exfoliated molybdenum disulfide (MoS2) connected to interdigitated metal electrodes were investigated. The MoS2 flake-based sensor detected a NO2 concentration as low as 1.2 ppm and exhibited excellent gas-sensing stability. Instead of metal(More)
In this paper we consider the hyperbolic Kac–Moody algebra F associated with the generalized Cartan matrix ( 2 −2 0 −2 2 −1 0 −1 2 ) . Its connection to Siegel modular forms of genus 2 was first studied by A. Feingold and I. Frenkel. The denominator function of F is not an automorphic form. However, Gritsenko and Nikulin extended F to a generalized(More)
In this paper, we decompose the set of fully commutative elements into natural subsets when the Coxeter group is of type Dn, and study combinatorics of these subsets, revealing hidden structures. (We do not consider type An first, since a similar decomposition for type An is trivial.) As an application, we classify and enumerate the homogeneous(More)