Let G be a (not necessarily finite) group and p a finite dimensional faithful irreducible representation of G over an arbitrary field; write ~p for p viewed as a projective representation. Suppose that p is not induced (from any proper subgroup) and that ~p~ is not a tensor product (of projective representations of dimension greater than 1 ). Let AT be a noncentral subgroup which centralizes al...

This paper gives a comprehensive analysis of the inverse problem of Lagrangian dynamics for the geodesic equations of the canonical linear connection on Lie groups of dimension four. Starting from the Lie algebra, in every case a faithful four-dimensional representation of the algebra is given as well as one in terms of vector fields and a representation of the linear group of which the given a...

The Jones–Witten theory gives rise to representations of the (extended) mapping class group of any closed surface Y indexed by a semi-simple Lie group G and a level k . In the case G = SU(2) these representations (denoted VA(Y )) have a particularly simple description in terms of the Kauffman skein modules with parameter A a primitive 4r root of unity (r = k + 2). In each of these representatio...

The paper asks whether diagrams in mathematics are particularly fruitful compared to other types of representations. In order to respond to this question a number of examples of propositions and their proofs are considered. In addition I use part of Peirce’s semiotics to characterise different types of signs used in mathematical reasoning, distinguishing between symbolic expressions and 2-dimen...

In this article we construct an irreducible simple subgroup G = 〈q, y, t, w〉 of GL8671(13) from an irreducible subgroup T of GL11(2) isomorphic to Mathieu’s simple group M24 by means of Algorithm 2.5 of [13]. We also use the first author’s similar construction of Fischer’s sporadic simple group G1 = Fi23 described in [11]. He starts from an irreducible subgroup T1 of GL11(2) contained in T whic...

Over time, there have been refinements in the way that probability distributions are used for representing beliefs. Models which rely on single probability distnlnrti ons depict a complete ordering among the propositions of interest, yet human beliefs are sometimes not completely ordered. Non-singleton sets of probability distributions can represent partially ordered beliefs. Convex sets are pa...

In the last papers published by Alchourrón, he attacked non-monotonic logics, which he considered philosophically unsound for the representation of defeasible reasoning. Instead of a non-monotonic consequence relation, he proposed a formal representation of defeasibility based on an AGM-like revision of implicit assumptions connected to the premises. Given that this is a procedure to generate n...