A canonical form for a symplectic involution

The Discriminant of a Decomposable Symplectic Involution

A formula is given for the discriminant of the tensor product of the canonical involution on a quaternion algebra and an orthogonal involution on a central simple algebra of degree divisible by 4. As an application, an alternative proof of Shapiro’s “Pfister Factor Conjecture” is given for tensor products of at most five quaternion algebras. Throughout this paper, the characteristic of the base...

The Discriminant of a Symplectic Involution

An invariant for symplectic involutions on central simple algebras of degree divisible by 4 over fields of characteristic different from 2 is defined on the basis of Rost’s cohomological invariant of degree 3 for torsors under symplectic groups. We relate this invariant to trace forms and show how its triviality yields a decomposability criterion for algebras with symplectic involution.

Anti-symplectic Involution and Maslov Indices

We carry out some first steps in setting up a theory for Lagrangian Floer theory, mimicking Seidel’s construction for Hamiltonian Floer homology [7], for the subgroup HamL(M,ω) of Ham(M,ω) which preserves the Lagrangian L. When the symplectic manifold M has anti-symplectic involution c and L is the fixed Lagrangian submanifold, we consider the subgroup Hamc(M,ω) which commute with c. In the lat...

A Canonical Form for Circuit Diagrams

A canonical form for circuit diagrams with a designated start state is presented. The form is based upon nite automata minimization and Shannon's canonical form for boolean expressions.

A Rational Canonical Form Algorithm