We prove that if ▫$p$▫ is a prime, ▫$p)3$▫, and ▫$G$▫ is a group of order ▫$p^5$▫ not belonging to the 10-th isoclinism family, then the unramified Brauer group of ▫$G$▫ is trivial.
COBISS.SI-ID: 16521049
Let ▫$H$▫ be an infinite dimensional separable complex Hilbert space and ▫${\cal U}$▫ be the group of all unitary operators on $H$. Motivated by the algebraic properties of surjective isometries of ▫$\cal U$▫ that have recently been revealed, and also by some classical results related to automorphisms of the unitary groups of operator algebras, we determine the structures of bijective transformations of ▫$\cal U$▫ that respect certain algebraic operations. These are, among others, the usual product of operators, the Jordan triple product, the inverted Jordan triple product, and the multiplicative commutator. Our basic approach to obtain these results is the use of commutativity preserving transformations on the unitary group.
COBISS.SI-ID: 16568153
We describe the structure of all continuous sequential endomorphisms of the effect algebra of a finite-dimensional Hilbert space.
COBISS.SI-ID: 16197209