‎The Lorentz transformation of order $(m=1,n)$‎, ‎$ninNb$‎, ‎is the well-known ‎Lorentz transformation of special relativity theory‎. ‎It is a transformation of time-space coordinates of the ‎pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and ‎$n$ space dimensions ($n=3$ in physical applications)‎. ‎A Lorentz transformation without rotations is called a {it boost}‎. ‎Commonly‎, ‎the ...

Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

Suppose M is an n-dimensional Kähler manifold and L is an ample line bundle over M . Let the Kähler form of M be ωg and the Hermitian metric of L be H. We assume that ωg is the curvature of H, that is, ωg = Ric(H). The Kähler metric of ωg is called a polarized Kähler metric on M . Using H and ωg, for any positive integer m, H 0(M,Lm) becomes a Hermitian inner product space. We use the following...

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

The calculus of generalized p-forms,−1 p n, is developed further. On an n-dimensional manifold with metric, M, a (Hodge) star operator, inner product, co-differential and Laplacian operators are introduced. The inner product and Lie derivative with respect to vector fields on M are defined. Applications are made to Hamiltonian mechanics, field theories and Einstein’s vacuum equations. PACS numb...