We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.

In this paper we completely characterize lattice ideals that are complete intersections or equivalently complete intersections finitely generated semigroups of ZZn ⊕ T with no invertible elements, where T is a finite abelian group. We also characterize the lattice ideals that are set-theoretic complete intersections on binomials.

A q-analogue of de Finetti’s theorem is obtained in terms of a boundary problem for the q-Pascal graph. For q a power of prime this leads to a characterisation of random spaces over the Galois field Fq that are invariant under the natural action of the infinite group of invertible matrices with coefficients from Fq.

We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices.

This paper studies a q-deformation, Br,s(q), of the walled Brauer algebra (a certain subalgebra of the Brauer algebra) and shows that the centralizer algebra for the action of the quantum group UR(gln) on mixed tensor space (R) ⊗ (Rn)∗ is generated by the action of Br,s(q) for any commutative ring R with one and an invertible element q.

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

We show that several problems which are known to be undecidable for probabilistic automata become decidable for quantum finite automata. Our main tool is an algebraic result of independent interest: we give an algorithm which, given a finite number of invertible matrices, computes the Zariski closure of the group generated by these matrices.

We prove the formula ed(X ) = cdim(X ) + ed(A) for any gerbe X banded by an algebraic group A which is the kernel of a homomorphism of algebraic tori Q → S with Q invertible and S split. This result is applied to prove new results on the essential dimension of algebraic groups.

A graded tensor category over a group G will be called a strongly G-graded tensor category if every homogeneous component has at least one invertible object. Our main result is a description of the module categories over a strongly G-graded tensor category as induced from module categories over tensor subcategories associated with the subgroups of G.

Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key additions. The bijectivity of any encryption function, crucial in order to make the decryption possible, is guaranteed by the use of invertible laye...