Related papers: Linear representations of formal loops

In this paper we consider representations of certain combinatorial categories, including the poset $\D$ of positive integers and division, the Young lattice $\mathscr{Y}$ of partitions of finite sets, the opposite category of the orbit…

In this work we construct free Moufang loop in the variety generated by code loops. We apply this construction for study the code loops. Moreover, we define and determine all basic representations of code loops of rank 3 and 4.

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

We give a characterization of the sets of objects of the derived category of a block of a finite group algebra (or other symmetric algebra) that occur as the set of images of simple modules under an equivalence of derived categories. We…

For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…

The set of formal power series with coefficients in an associative but noncommutative algebra becomes a loop with the substitution product. We initiate the study of this loop by describing certain Lie and Sabinin algebras related to it.…

Moufang loops are one of the best-known generalizations of groups. There is only one countable family of nonassociative finite simple Moufang loops, arising from the split octonion algebras. We prove that every member of this family is…

We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…

Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…

In this note we show that similar to the classical case the ring of representations of symmetric groups in a tensor derived category is certain ring of symmetric functions. We also show that in the general setting considered here, the Adams…

In this paper it is stressed that there is no {\em physical} reason for symmetries to be linear and that Lie group theory is therefore too restrictive. We illustrate this with some simple examples. Then we give a readable review on the…

An equivalent description of a symmetric monoidal category is introduced in which, instead of separate associator and commutator isomorphisms satisfying the usual coherence axioms, we simply have associo-commutator isomorphisms satisfying…

We propose an alternative representation for linear quantum gravity. It is based on the use of a structure that bears some resemblance to the Abelian loop representation used in electromagnetism but with the difference that space of…

We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…

We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…

Two Lie algebroids are presented that are linked to the construction of the linearizing output of an affine in the input nonlinear system. The algorithmic construction of the linearizing output proceeds inductively, and each stage has two…

We introduce a formalism of infinite, linearly ordered products in general groups. Using this, we define infinite compositions in certain groups of formal power series such as transseries. We show that such groups can sometimes be…

We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects and discuss some of the standard constructions from representation theory in this…