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Quotient structures in lattice effect algebras

Amir Hossein Sharafi, Rajb Ali Borzooei (2019)

Kybernetika

In this paper, we define some types of filters in lattice effect algebras, investigate some relations between them and introduce some new examples of lattice effect algebras. Then by using the strong filter, we find a CI-lattice congruence on lattice effect algebras, such that the induced quotient structure of it is a lattice effect algebra, too. Finally, under some suitable conditions, we get a quotient MV-effect algebra and a quotient orthomodular lattice, by this congruence relation.

Seeable matter; unseeable antimatter

Geoffrey Dixon (2014)

Commentationes Mathematicae Universitatis Carolinae

The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra 𝐓 : = 𝐂 ⊗ 𝐇 ⊗ 𝐎 , an interpretation is developed that suggests that this seeable universe is not the whole universe; there is an unseeable part of the universe composed of antimatter galaxies and stuff, and an extra 6 dimensions of space (also unseeable) linking the matter side to the antimatter—at the very least.

Spectrum generating functions for oscillators in Wigner's quantization

Stijn Lievens, Joris Van der Jeugt (2011)

Banach Center Publications

The n-dimensional (isotropic and non-isotropic) harmonic oscillator is studied as a Wigner quantum system. In particular, we focus on the energy spectrum of such systems. We show how to solve the compatibility conditions in terms of 𝔬𝔰𝔭(1|2n) generators, and also recall the solution in terms of 𝔤𝔩(1|n) generators. A method is described for determining a spectrum generating function for an element of the Cartan subalgebra when working with a representation of any Lie (super)algebra. Here, the...

Symmetric quantum Weyl algebras

Rafael Díaz, Eddy Pariguan (2004)

Annales mathématiques Blaise Pascal

We study the symmetric powers of four algebras: q -oscillator algebra, q -Weyl algebra, h -Weyl algebra and U ( 𝔰𝔩 2 ) . We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.

Ternary symmetries and the Lorentz group

Richard Kerner (2011)

Banach Center Publications

We show that the Lorentz and the SU(3) groups can be derived from the covariance principle conserving a Z₃-graded three-form on a Z₃-graded cubic algebra representing quarks endowed with non-standard commutation laws. The ternary commutation relations on an algebra generated by two elements lead to cubic combinations of three quarks or antiquarks that transform as Lorentz spinors, and binary quark-anti-quark combinations that transform as Lorentz vectors.

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