A generalization of the matrix transpose map and its relationship to the twist of the polynomial ring by an automorphism

@article{McGinnis2017AGO,
title={A generalization of the matrix transpose map and its relationship to the twist of the polynomial ring by an automorphism},
author={Andrew M. McGinnis and Michaela Vancliff},
journal={Involve, A Journal of Mathematics},
year={2017},
volume={10},
pages={43-50}
}

A generalization of the notion of symmetric matrix was introduced by Cassidy and Vancliff in 2010, and used by them in a construction that produces quadratic regular algebras of finite global dimension that are generalizations of graded Clifford algebras. In this article, we further their ideas by introducing a generalization of the matrix transpose map and use it to generalize the notion of skew-symmetric matrix. With these definitions, an analogue of the result that every n × n matrix is a… Expand

For decades, the study of graded Clifford algebras has provided a theory where commutative algebraic geometry has dictated the algebraic and homological behavior of a noncommutative algebra. In… Expand

In 2010, a quantized analog of a graded Clifford algebra (GCA), called a graded skew Clifford algebra (GSCA), was proposed by Cassidy and Vancliff, and many properties of GCAs were found to have… Expand

In 2010, Cassidy and Vancliff extended the notion of a quadratic form on n generators to the noncommutative setting. In this article, we suggest a notion of rank for such noncommutative quadratic… Expand

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)… Expand