We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface. Introduction It is by now well known that a direct sum ⊕ n≥0R(Sn) of the Grothendieck rings of symmetric groups Sn can be identified with the Fock space of the Hei...

Min-plus convolution is an algebra system that has applications to computer networks. Mathematically, the identity of min-plus convolution plays a key role in theory. On the other hand, the mathematical representation of the identity, which is computable with digital computers, is essential for further developing min-plus convolution (e.g., de-convolution) in practice. However, the identical el...

Guided by the construction of the unital *-algebra of closed operators which are ‘affiliated’ with a given unital *-algebra, we introduce the notion of the ‘monotone closure’ for certain increasing sequences of unital *-algebras. Then we study an example of a unital *-algebra F0(A) constructed from a countable number of copies of a unital *-algebra A. We endow F0(A) with a quantum semigroup str...

Patras, Reutenauer (J. Algebr. Comb. 16:301–314, 2002) describe a subalgebra A of the Malvenuto-Reutenauer algebra P . Their paper contains several characteristic properties of this subalgebra. In an unpublished manuscript Manfred Schocker states without proof a theorem, providing two further characterizations of the Patras-Reutenauer algebra. In this paper we establish a slightly generalized v...

We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantum field theory. We introduce a convolution product and a semigroup of characters of this Hopf algebra with values in some suitable commutative algebra taking momenta into account. We then implement the renormalization described by A. Connes and D. Kreimer in [2] and the Birkhoff decomposition for two renor...

Many interesting C∗-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution C∗-algebra of a symplectic groupoid. Toward this end, I define polarizations for Lie groupoids and sketch the construction of this algebra. A large number of examples show that this idea unifies previous geometric constructions, ...

In this paper we study a q-analogue of the convolution product on the line in detail. A convolution product on the braided line was defined algebraically by Kempf and Majid. We adapt their definition in order to give an analytic definition for the q-convolution and we study convergence extensively. Since the braided line is commutative as an algebra, all results can be viewed both as results in...

We present algorithms for computing the probablity density function of the sum of two independent discrete random variables, along with an implementation of the algorithm in a computer algebra system. Some examples illustrate the utility of this algorithm. c © 2004 Elsevier Science Ltd. All rights reserved. Keywords—Computer algebra systems, Convolution, Probability.

A coplactic class in the symmetric group Sn consists of all permutations in Sn with a given Schensted Q-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of Sn which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Re...