Generalized Clifford algebras, weighted polynomial laws, and adjunction

2025/10/08 by Bach, Nguyen Xuan
#Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2510.06560

Abstract

In this paper, we study Clifford algebra construction from the perspective of adjunctions motivated by the general framework of Krashen and Lieblich. We introduce a category of weighted polynomial laws whose associated Clifford algebra functor is a left adjoint on this category. We introduce a notion of lifting weighted polynomial laws generalizing explicit constructions of Krashen and Lieblich. As another application, we construct derived Clifford algebras of derived homogeneous polynomial forms of arbitrary degree with noncommutative coefficients.

Citations

• Revisiting derived crystalline cohomology
• Purity for flat cohomology
• The Clifford algebra of a finite morphism
• On the generalized Clifford algebra of a monic polynomial
• Derived Algebraic Geometry II: Noncommutative Algebra
• Quasi-perfect scheme-maps and boundedness of the twisted inverse image\n functor
• Higher Topos Theory
• Linear maximal Cohen-Macaulay modules over strict complete intersections

Related

• Clifford algebra, geometric algebra, and applications
• Skew Clifford Algebras
• Formalizing Polynomial Laws and the Universal Divided Power Algebra
• On the generalized Clifford algebra of a monic polynomial
• Álgebras y grupos de Clifford, espinores algebraicos y aplicaciones a la física