Let A be a finite dimensional Hopf algebra, D(A) = A ⊗A its Drinfel’d double and H(A) = A#A its Heisenberg double. The relation between D(A) and H(A) has been found by J.-H. Lu in [24] (see also [33], p. 196): the multiplication of H(A) may be obtained by twisting the multiplication of D(A) by a certain left 2-cocycle which in turn is obtained from the R-matrix of D(A). It was also obtained in ...

The centralizer algebra of the action of U(n) on the real tensor powers ⊗RV of its natural module, V = Cn, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for U(n) and with the decomposition of ⊗RV into irreducible submodules is considered.

Abstract. We study h-vectors and graded Betti numbers of level modules up to multiplication by a rational number. Assuming a conjecture on the possible graded Betti numbers of Cohen-Macaulaymodules we get a description of the possible h-vectors of level modules up to multiplication by a rational number. We also determine, again up to multiplication by a rational number, the cancellable h-vector...

The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF (q), where q = p k and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1], the US federal Digital Signature Standard [2], elliptic curve cryptography [3, 4], and also recently identity based cryptography [5, 6]. Most p...

Let κ be an U-invariant reproducing kernel and let H (κ) denote the reproducing kernel Hilbert C[z1, . . . , zd]-module associated with the kernel κ. Let Mz denote the d-tuple of multiplication operators Mz1 , . . . ,Mzd on H (κ). For a positive integer ν and d-tuple T = (T1, . . . , Td), consider the defect operator

Let κ be an U-invariant reproducing kernel and let H (κ) denote the reproducing kernel Hilbert C[z1, . . . , zd]-module associated with the kernel κ. Let Mz denote the d-tuple of multiplication operators Mz1 , . . . ,Mzd on H (κ). For a positive integer ν and d-tuple T = (T1, . . . , Td), consider the defect operator

Lerch’s formulae for Euler quotients in the rings Z and Fq[t] have already been studied. In this paper, we extend the study of these quotients to number fields and the Carlitz module. In the number fields case, we prove a version of Lerch’s formula for OKHil , the ring of integers of the Hilbert class field of a number field K. In the Fq[t] case, we replace the usual multiplication in Fq[t] wit...

In this paper, we present a protocol for a ID-based signature scheme using a tamperresistant module that holds a private key for signing. This is a distributed-signature scheme, and a computation using a private key is executed on the tamper-resistant module (TRM), with the remaining computations performed on a host PC. The scheme is secure against both passive and active adversaries, even thos...

This paper présents a new approach for multi-objective optimization of area-delay-power simultaneously for VLSI implementation of digital finite impulse response filter. It is based on use of concept of multiple constant multiplication approach with partial product sharing and coefficient reuse in multiplier module and /or digit serial architecture in adder module design along with fixed point ...

This paper is concerned with finite unions of ideals and modules. The first main result is that if N ⊆ N1 ∪N2 ∪ · · · ∪Ns is a covering of a module N by submodules Ni, such that all but two of the Ni are intersections of strongly irreducible modules, then N ⊆ Nk for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on co...