Embedding theorems as a bridge between supertraces and supergeometry

2025/06/25 by Charles Almeida, Lucio Centrone, Almeida, Charles +3
Computer Science · Mathematics · #14L15 #16R30 #16W55 #17A05 #17A50 #Advanced Graph Theory Research #Advanced Topics in Algebra #FOS: Mathematics #Mathematics and Applications #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2506.20395

openalex publication_date 2025/06/25 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

Any algebra herein is intended over a field of characteristic 0. Let E denote the infinite dimensional Grassman algebra. Given a power associative finite dimensional ℤ₂-graded-central-simple A and a supertrace algebra B, so that B belongs to the same variety of A⊗ E, we study conditions on B so that it can be embedded into A⊗Ξ, where Ξ is a supercommutative algebra, called A-universal supermap of B, provided B satisfies all the supertrace identities of A⊗ E. We use this result in order to relate the formal smoothness of B with that of its A-universal supermap.

Citations

• Automorphisms and superalgebra structures on the Grassmann algebra
• On the notion of Krull super-dimension
• Composition algebras
• Invariants of G₂ and Spin(7) in positive characteristic
• On Z2-graded polynomial identities of the Grassmann algebra
• Representability and Specht problem for G-graded algebras
• A formal inverse to the Cayley-Hamilton theorem
• The invariant theory of n × n matrices

Related

• Superpolynomial identities of finite-dimensional simple algebras
• Automorphisms and superalgebra structures on the Grassmann algebra
• Homotopy Classification of Super Vector Bundles and Universality
• Interplay between ℤ₂-gradings and automorphisms in the Grassmann algebra: a survey
• Universal Super Vector Bundles