Norms and Cayley Hamilton algebras

Remarks on the Cayley-Hamilton Theorem

We revisit the classical theorem by Cayley and Hamilton, "{\em each endomorphism is a root of its own characteristic polynomial}", from the point of view of {\em Hasse--Schmidt derivations on an exterior algebra}

Grassman semialgebras and the Cayley-Hamilton theorem

We develop a theory of semialgebra Grassmann triples via Hasse-Schmidt derivations, which formally generalizes results such as the Cayley-Hamilton theorem in linear algebra, thereby providing a unified approach to classical linear algebra and tropical algebra.

Cayley Hamilton代数与Skip Garibaldi的一篇论文

Cayley Hamilton algebras and a paper by Skip Garibaldi

本文基于Skip Garibaldi的相关论文，针对域上有限维代数，开展了最小Cayley Hamilton范数的讨论研究。

Hasse--Schmidt Derivations and Cayley--Hamilton Theorem for Exterior Algebras

Using the natural notion of {\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, "{\em each endomorphism of a finite-dimensional vector space is a root of its own characteristic polynomial}", and the second concerns the expression of the bosonic vertex operators occurring in the representation theory of the (infinite-dimensional) Heinsenberg algebra.

Root of unity quantum cluster algebras and Cayley-Hamilton algebras

We prove that large classes of algebras in the framework of root of unity quantum cluster algebras have the structures of maximal orders in central simple algebras and Cayley-Hamilton algebras in the sense of Procesi. We show that every root of unity upper quantum cluster algebra is a maximal order and obtain an explicit formula for its reduced trace. Under mild assumptions, inside each such algebra we construct a canonical central subalgebra isomorphic to the underlying upper cluster algebra, such that the pair is a Cayley-Hamilton algebra; its fully Azumaya locus is shown to contain a copy o…

Cayley-Hamilton Hopf代数的最低判别理想

The lowest discriminant ideal of a Cayley-Hamilton Hopf algebra

本文研究了Cayley-Hamilton Hopf代数的最低判别理想，用极大稳定模描述其零点集，并揭示其受winding自同构群作用支配，应用于群代数及量子代数等实例。