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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Radii and centers in iterated line digraphs

100%
Knor M., Niepel L. u.
Discussiones Mathematicae Graph Theory
|
1996
|
tom 16
|
nr 1
17-26
EN
We show that the out-radius and the radius grow linearly, or "almost" linearly, in iterated line digraphs. Further, iterated line digraphs with a prescribed out-center, or a center, are constructed. It is shown that not every line digraph is admissible as an out-center of line digraph.
2
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Center of the algebra of functions on the quantum group \(\mathrm{SU}_q(2)\) and related topics

100%
Krajczok J., Sołtan P.
Commentationes Mathematicae
|
2016
|
tom 56
|
nr 2
EN
The center of the algebra of continuous functions on the quantum group \(\mathrm{SU}_q(2)\) is determined as well as centers of other related algebras. Several other results concerning this quantum group are given with direct proofs based on concrete realization of these algebras as algebras of operators on a Hilbert space.
3
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The exocenter and type decomposition of a generalized pseudoeffect algebra

75%
Foulis D., Pulmannová S., Vinceková E.
Discussiones Mathematicae - General Algebra and Applications
|
2013
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tom 33
|
nr 1
13-47
EN
We extend the notion of the exocenter of a generalized effect algebra (GEA) to a generalized pseudoeffect algebra (GPEA) and show that elements of the exocenter are in one-to-one correspondence with direct decompositions of the GPEA; thus the exocenter is a generalization of the center of a pseudoeffect algebra (PEA). The exocenter forms a boolean algebra and the central elements of the GPEA correspond to elements of a sublattice of the exocenter which forms a generalized boolean algebra. We extend the notion of central orthocompleteness to GPEA, prove that the exocenter of a centrally orthocomplete GPEA (COGPEA) is a complete boolean algebra and show that the sublattice corresponding to the center is a complete boolean subalgebra. We also show that in a COGPEA, every element admits an exocentral cover and that the family of all exocentral covers, the so-called exocentral cover system, has the properties of a hull system on a generalized effect algebra. We extend the notion of type determining (TD) sets, originally introduced for effect algebras and then extended to GEAs and PEAs, to GPEAs, and prove a type-decomposition theorem, analogous to the type decomposition of von Neumann algebras.
4
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Minimal non-selfcentric radially-maximal graphs of radius 4

75%
Knor M.
Discussiones Mathematicae Graph Theory
|
2007
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tom 27
|
nr 3
603-610
EN
There is a hypothesis that a non-selfcentric radially-maximal graph of radius r has at least 3r-1 vertices. Using some recent results we prove this hypothesis for r = 4.
5
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A note on semidirect sum of Lie algebras

63%
Ostrowski T.
Discussiones Mathematicae - General Algebra and Applications
|
2013
|
tom 33
|
nr 2
233-247
EN
In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well.
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