We present a practical algorithm to construct the subgroup of the general linear group that preserves a system of bilinear or sesquilinear forms on a vector space defined over a finite field. Components include efficient algorithms to construct the Jacobson radical and the group of units of a matrix algebra.

Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear formswithout any symmetry property. The present paperwill establish aWitt cancellation result, an analogue of Springer’s theorem, as well as some local–global and finiteness results in this context. © 2013 Elsevier B.V. All...

Let L be a degree 2 Galois extension of the field K and M an n×n matrix with coefficients in L. Let 〈 , 〉 : Ln × Ln −→ L be the sesquilinear form associated to the involution L −→ L fixing K. We use 〈 , 〉 to define the numerical range Num(M) of M (a subset of L), extending the classical case K = R, L = C and the case of a finite field introduced by Coons, Jenkins, Knowles, Luke and Rault. There...

Many classical results concerning quadratic forms have been extended to hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cancellation result, an analogue of Springer’s theorem, as well as some local-global and finiteness results in this context. Mathematics Subject C...

We describe the structure of the subgroup of the general linear group defined over a finite field that preserves two bilinear or sesquilinear forms of the same classical type, at least one of which is non-degenerate. This description underpins an algorithm to construct the intersection of two classical groups of the same type.

We study Lp-theory of second order elliptic divergence type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C0-semigroups on Lp associated with sesquilinear (not necessarily sectorial) forms in L2. A precise condition ensuring that the elliptic operator is associated with a quasi-contractive C0-semigroup on Lp is established.