2023/04/16 by Garrel, Nicolas
#11E81 #12G05 #16W70 #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2304.07807
We extend all cohomological invariants of similarity classes of quadratic forms to anti-hermitian forms over a quaternion algebra. This uses the fact that such invariants can be lifted to Witt invariants, which can be described as combinations of λ-operations, and those λ-operations have recently been extended to hermitian forms over algebras with involution. In the article we present a detailed combinatoric description of invariants of quadratic forms which are partially diagonalized, and show how this combinatorics extend to anti-hermitian quaternionic forms. The methods developped here are intended to be later used for general algebras with involution.