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- W2911806688 abstract "We introduce an associative algebra Mk(x) whose dimension is the 2k-th Motzkin number. The algebra Mk(x) has a basis of “Motzkin diagrams”, which are analogous to Brauer and Temperley–Lieb diagrams. We show for a particular value of x that the algebra Mk(x) is the centralizer algebra of the quantum enveloping algebra Uq(gl2) acting on the k-fold tensor power of the sum of the 1-dimensional and 2-dimensional irreducible Uq(gl2)-modules. We prove that Mk(x) is cellular in the sense of Graham and Lehrer and construct indecomposable Mk(x)-modules which are the left cell modules. When Mk(x) is a semisimple algebra, these modules provide a complete set of representatives of isomorphism classes of irreducible Mk(x)-modules. We compute the determinant of the Gram matrix of a bilinear form on the cell modules and use these determinants to show that Mk(x) is semisimple exactly when x is not the root of certain Chebyshev polynomials." @default.
- W2911806688 created "2019-02-21" @default.
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- W2911806688 date "2014-02-01" @default.
- W2911806688 modified "2023-10-16" @default.
- W2911806688 title "Motzkin algebras" @default.
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- W2911806688 doi "https://doi.org/10.1016/j.ejc.2013.09.010" @default.
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