Let A be a definite quaternion algebra over ℚ, with discriminant D , and

It is often inevitable to introduce an indefinite-metric space in quantum field theory, for example, which is explained for the sake of the manifestly covariant quantization of the electromagnetic field. We show two more evident mathematical reasons why such indefinite metric appears. The first idea is the replacement of involution on an algebra. For an algebra A with an involution † such that ...

Let $X$ be a finitistic space with the mod $2$ cohomology of product projective and $4$-sphere. Assume that admits free involution. In this paper we study algebra quotient by action involution derive some consequences regarding existence $\mathbb{Z}\_2$-equivariant maps between such an $n$-sphere.

The quaternion Fourier transform (QFT), which is a nontrivial generalization of the real and complex Fourier transform (FT) using quaternion algebra has been of interest to researchers for some years (see e.g. [3, 5]). It was found that many FT properties still hold but others have to be modified. Based on the (right-sided) QFT, one can extend the classical wavelet transform (WT) to quaternion ...

In the present paper it is proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero minimal fixed *-graded exponent if, and only generated by subalgebra an upper block triangular matrix algebra equipped suitable elementary ?2-grading involution.

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...

Two Banach algebras are naturally associated with a locally compact group G: the group algebra, L,(G), and the measure algebra, M(G). For these two Banach algebras we determine all isometric involutions. Each of these Banach algebras has a natural involution. We will show that an isometric involution, (*), is the natural involution on £'(<?) if and only if the closure in the strict topology of ...