Geometric algebra is a useful tool to overcome some problems in kinematics. Thus, the geometric has attracted attention of many researchers. In this paper, quaternion operators on curves and surfaces Euclidean 3-space are defined by using algebra. These generate or from points, surfaces. Using operators, we obtain motions that have orbits along generated curve surface. Also, these expressed as ...

Fixing a field F of characteristic different from 2 and 3, we consider pairs (A, V ) consisting of a degree 3 central simple F -algebra A and a 3-dimensional vector subspace V of the reduced trace zero elements of A which is totally isotropic for the trace quadratic form. Each such pair gives rise to a cubic form mapping an element of V to its cube; therefore we call it a cubic pair over F . Us...

Our task here is to recall part of the theory of orders and ideals in quaternion algebras. Some of the theory makes sense in the context of B/K a quaternion algebra over a field K which is the quotient field of a Dedekind ring R. For our purposes K will always be a number field, or the completion of a number field at a finite prime, and R will be the ring of integers of K. (Nevertheless, we sha...

In this paper we prove a version of Mordell’s inequality for lattices in finite-dimensional complex or quaternionic Hermitian space that are modules over a maximal order in an imaginary quadratic number field or a totally definite rational quaternion algebra. This inequality implies that 16dimensional Barnes-Wall lattice has optimal density among all 16-dimensional lattices with Hurwitz structu...

The completion A[τ ] of a locally convex ∗-algebra A[τ ] with not jointly continuous multiplication is a ∗-vector space with partial multiplication xy defined only for x or y ∈ A0, and it is called a topological quasi ∗-algebra. In this paper two classes of topological quasi ∗-algebras called strict CQ-algebras and HCQ-algebras are studied. Roughly speaking, a strict CQ-algebra (resp. HCQ-algeb...

We consider a central division algebra over a separable quadratic extension of a base field endowed with a unitary involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. The remaining related projective homogeneous varieties are shown to be 2-compressible in general. Together with [17], where a similar issue for orthogonal and symplectic involuti...