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6 papers · 1 filter
Braid semistatistics and doubly regular R-matrix
S. Duplij, W. Marcinek
We introduce "noninvertible" generalization of statistics - semistatistics replacing condition when double exchanging gives identity to "regularity" condition. Then in categorical…
Particles of generalized statistics, quantum logic and categories
W. Marcinek
A collection of brilliant and original unfinished ideas by Wladyslaw Marcinek (1952-2003) in particle interactions, categorical approach to generalized statistics, qubits and quant…
Quantum Yang-Baxter equation, arbitrary gradings and exchange Hecke braidings
W. Marcinek
Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is consider…
Basic concepts of ternary Hopf algebras
Andrzej Borowiec, Wieslaw A. Dudek, Steven Duplij
The theory of ternary semigroups, groups and algebras is reformulated in the abstract arrow language. Then using the reversing arrow ansatz we define ternary comultiplication, bial…
Quantum-Classical Interactions and Galois Type Extensions
Wladyslaw Marcinek
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of pos…
Quantum-Classical Correspondence and Galois Extensions
Wladyslaw Marcinek
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category o…