The characteristic polynomial of an algebra and representations

2015/07/30 by Kulkarni, Rajesh S., Mustopa, Yusuf, Shipman, Ian
#16G10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1507.08361

Abstract

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result can be applied to study representations of higher-degree Clifford algebras and finite extensions of commutative rings.

Related

• Endomorphisms preserving coordinates of polynomial algebras
• Clifford correspondence for algebras
• Semi-characteristic polynomials, ϕ-modules and skew polynomials
• When a C*-algebra is a coefficient algebra for a given endomorphism
• On Clifford Algebras of Infinite Dimensional Vector Spaces