Previously, we have shown that the CAR algebra for fermions is embedded in the Cuntz algebra O2 in such a way that the generators are expressed in terms of polynomials in the canonical generators of the latter, and it coincides with the U(1)-fixed point subalgebra A ≡ O 2 of O2 for the canonical gauge action. Based on this embedding formula, some properties of A are studied in detail by restric...

Logical systems are represented in LF by giving a full and faithful (adequate) embedding of the deductive apparatus of the logic as canonical forms of certain types and kinds in LF in specified contexts. The collection of contexts over which the representation is adequate is called a world, because it provides generators for the canonical forms in question. Transferring adequacy from one world ...

This paper presents a novel treatment of the canonical extension of a bounded lattice, in the spirit of the theory of natural dualities. At the level of objects, this can be achieved by exploiting the topological representation due to M. Ploščica, and the canonical extension can be obtained in the same manner as can be done in the distributive case by exploiting Priestley duality. To encompass ...

Geometric complexity theory (GCT) is an approach to P vs. NP and related problems in complexity theory using algebraic geometry and representation theory. A fundamental problem in representation theory, believed to be important for this approach, is the Kronecker problem, which asks for a positive combinatorial formula for the multiplicity gλμν of an irreducible representation Mν of the symmetr...

The LF logical framework codifies a methodology for representing deductive systems, such as programming languages and logics, within a dependently typed λ-calculus. In this methodology, the syntactic and deductive apparatus of a system is encoded as the canonical forms of associated LF types; an encoding is correct (adequate) if and only if it defines a compositional bijection between the appar...

The well-known classification of the Clifford algebrasCl(r, s) leads to canonical forms of complex and real representations which are essentially unique by virtue of the Wedderburn theorem. For s ≥ 1 representations of Cl(r, s) on R are obtained from representations on R by adding two new generators while in passing from a representation of Cl(p, 0) on R to a representation of Cl(r, 0) on R the...

Stack caching speeds Forth up by keeping stack items in registers, reducing the number of memory accesses for stack items. This paper describes our work on extending Gforth’s stack caching implementation to support more than one register in the canonical state, and presents timing results for the resulting Forth system. For single-representation stack caches, keeping just one stack item in regi...

This paper studies matrix fractional representation for impulse responses of a certain class of infinite-dimensional linear systems which contains, in particular, delay-differential systems. Such impulse responses are called pseudo-rational in this paper. This fractional representation is effectively used to derive concrete function space models from the abstract shift realizations. Given a fra...