Horrocks theorem for odd orthogonal groups

2025/06/12 by A, Ambily A, H, Sugilesh
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2506.10360

Abstract

We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring R[X], over a commutative ring R in which 2 is invertible, as a product of an orthogonal matrix with entries in R and an elementary orthogonal matrix with entries from R[X].

Citations

• Normality of DSER elementary orthogonal group
• Extendability of quadratic modules over a polynomial extension of an equicharacteristic regular local ring

Related

• Yoga of Commutators in Roy's Elementary Orthogonal Group
• Visualization for Petrov's Odd Unitary Group
• Generalised homotopy and commutativity principle
• Normality and K₁-stability of Roy's elementary orthogonal group
• Groups with BC_ℓ-commutator relations