16 research outputs found
Presenting Schur superalgebras
We provide a presentation of the Schur superalgebra and its quantum analogue
which generalizes the work of Doty and Giaquinto for Schur algebras. Our
results include a basis for these algebras and a presentation using weight
idempotents in the spirit of Lusztig's modified quantum groups.Comment: 28 pages, to appear in the Pacific Journal of Mathematic
Complexity of Modules over Lie Superalgebras
In this dissertation, a fair amount of work is dedicated to computing the complexity of modules over a classical Lie superalgebra \fg=\fg_{\0}\oplus \fg_{\1} over the complex numbers \C. We will consider the category \F of finite dimensional \fg-supermodules which are completely reducible as \fg_{\0}-modules. Every module M\in \F admits a minimal projective resolution whose terms have dimensions which increase at a polynomial rate of growth. This rate of growth is called the \emph{complexity} of . In \cite{BKN1} the authors compute the complexity of the simple and the Kac modules over the general linear Lie superalgebra \gl(m|n) of type . A natural continuation to their work is computing the complexity of the same family of modules over the ortho-symplectic Lie superalgebra \osp(2|2n) of type . The two Lie superalgebras are both of \emph{Type I}, thus the Kac modules in the two cases are constructed by the same induction functor. This similarity will result in similar computations. In fact, our geometric interpretation of the complexity agrees with theirs. The complexity is not a categorical invariant. However, we compute a categorical invariant called the -complexity, introduced in \cite{BKN1}, and we interpret this invariant geometrically in terms of a specific detecting subsuperalgebra. In addition, we compute the complexity and the -complexity of the simple modules over the \emph{Type II} Lie superalgebras \osp(3|2), \dd, , and
Special Issue Call for Papers: Creativity in Mathematics
The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Creativity in Mathematics. Please send your abstract submissions via email to the guest editors by March 1, 2019. Initial submission of complete manuscripts is due August 1, 2019. The issue is currently scheduled to appear in July 2020
Inquiry as an Entry Point to Equity in the Classroom
Although many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity. In this paper, through aligning some characteristics of inquiry put forth by Cook, Murphy and Fukawa-Connelly with Gutiérrez\u27s dimensions of equity, we theoretically explore the ways in which active learning teaching practices that focus on inquiry could support equity in the classroom
Exploring Bounds for the Frobenius Number
Let G be a set of three natural numbers, G = {a, b, c}, such that
gcd(a, b, c) = 1. The Frobenius number of G is the largest integer that cannot
be written as a non-negative linear combination of elements of G. In this article,
we present some experimental results on the Frobenius number