The infinite matrix ‘Schwartz’ group G−∞ is a classifying group for odd K-theory and carries Chern classes in each odd dimension, generating the cohomology. These classes are closely related to the Fredholm determinant on G−∞. We show that while the higher (even, Schwartz) loop groups of G−∞, again classifying for odd K-theory, do not carry multiplicative determinants generating the first Chern...

The representation theory of finite groups began with Frobenius's factorization Dedekind's group determinant. In this paper, we consider the case semigroup determinant is nonzero if and only complex algebra Frobenius, so our results include applications to study Frobenius algebras. We explicitly factor for commutative semigroups inverse semigroups. recover Wilf-Lindström a meet semilattice Wood...

We study the determinants on the sum of orbits of two elements in the Lie algebra of a compact connected subgroup in the unitary group. As an application, the extremal determinant expressions are obtained for the symplectic group.

Analyzing agro-climatic conditions for the period of 1981–2020 has revealed a tendency local climate warming under condition its aridization in territory Central region Russian Non-Chernozem zone, and new northern borders soybean growing have been marked. The isotherm sum active temperatures established to shifted towards high latitudes by 150–200 km. values increased from 1700–2200 °C 1950–240...

We study implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into sub-determinants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple sub-determinant identity which has a non-trivial inte...

The transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some properties of the transfer by noncommutative determinant. As a result, we can understand the properties of the transfer more naturally.