Introduction to gb-Triple Systems

ISRN Algebra ◽

10.1155/2014/738154 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5 ◽

Cited By ~ 1

Author(s):

Guy Roger Biyogmam

Keyword(s):

Triple Systems ◽

Leibniz Algebras ◽

Algebraic Properties

This paper introduces the category of gb-triple systems and studies some of their algebraic properties. Also provided is a functor from this category to the category of Leibniz algebras.

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Lie triple systems and Leibniz algebras

Georgian Mathematical Journal ◽

10.1515/gmj-2020-2053 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Revaz Kurdiani

Keyword(s):

Lie Algebra ◽

Central Extension ◽

Triple System ◽

Leibniz Algebra ◽

Universal Central Extension ◽

Central Extensions ◽

Lie Triple System ◽

Triple Systems ◽

Leibniz Algebras ◽

Universal Central Extensions

AbstractThe present paper deals with the Lie triple systems via Leibniz algebras. A perfect Lie algebra as a perfect Leibniz algebra and as a perfect Lie triple system is considered and the appropriate universal central extensions are studied. Using properties of Leibniz algebras, it is shown that the Lie triple system universal central extension is either the universal central extension of the Leibniz algebra or the universal central extension of the Lie algebra.

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A class of Lie racks associated to symmetric Leibniz algebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498822502309 ◽

2021 ◽

pp. 2250230 ◽

Cited By ~ 1

Author(s):

Hamid Abchir ◽

Fatima-ezzahrae Abid ◽

Mohamed Boucetta

Keyword(s):

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Leibniz Algebras ◽

Algebraic Properties ◽

Necessary And Sufficient

We classify symmetric Leibniz algebras in dimensions 3 and 4 and we determine all associated Lie racks. Some of such Lie racks give rise to nontrivial topological quandles. We study some algebraic properties of these quandles and we give a necessary and sufficient condition for them to be quasi-trivial.

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On triple systems, in particular those with 13 elements

Electronic Notes in Discrete Mathematics ◽

10.1016/s1571-0653(05)00736-5 ◽

2000 ◽

Vol 3 ◽

pp. 1-5

Author(s):

H GROPP

Keyword(s):

Triple Systems

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Catalytic Activity of Binary and Triple Systems Based on Redox Inactive Metal Compound, LiSt and Additives of Monodentate Ligands-Modifiers: DMF, HMPA and PhOH, in Selective Ethylbenzene Oxidation with Dioxygen

Chemistry & Chemical Technology ◽

10.23939/chcht10.03.259 ◽

2016 ◽

Vol 10 (3) ◽

pp. 259-270

Author(s):

Ludmila Matienko ◽

◽

Larisa Mosolova ◽

Vladimir Binyukov ◽

Gennady Zaikov ◽

...

Keyword(s):

Catalytic Activity ◽

Triple System ◽

Metal Compound ◽

Ethylbenzene Oxidation ◽

Catalytic Systems ◽

Triple Systems ◽

Lithium Compound ◽

Mechanism Of Catalysis ◽

Monodentate Ligands

Mechanism of catalysis with binary and triple catalytic systems based on redox inactive metal (lithium) compound {LiSt+L2} and {LiSt+L2+PhOH} (L2=DMF or HMPA), in the selective ethylbenzene oxidation by dioxygen into -phenylethyl hydroperoxide is researched. The results are compared with catalysis by nickel-lithium triple system {NiII(acac)2+LiSt+PhOH} in selective ethylbenzene oxidation to PEH. The role of H-bonding in mechanism of catalysis is discussed. The possibility of the stable supramolecular nanostructures formation on the basis of triple systems, {LiSt+L2+PhOH}, due to intermolecular H-bonds, is researched with the AFM method.

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On solvable Leibniz algebras whose nilradical has characteristic sequence (m1,m2,m3)

Uzbek Mathematical Journal ◽

10.29229/uzmj.2018-3-1 ◽

2018 ◽

Vol 2018 (3) ◽

pp. 4-17

Author(s):

K.K. Abdurasulov ◽

Drew Horton ◽

U.X. Mamadaliyev

Keyword(s):

Characteristic Sequence ◽

Leibniz Algebras

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Formation rate of LB-1-like systems through dynamical interactions

Publications of the Astronomical Society of Japan ◽

10.1093/pasj/psaa021 ◽

2020 ◽

Vol 72 (3) ◽

Cited By ~ 3

Author(s):

Ataru Tanikawa ◽

Tomoya Kinugawa ◽

Jun Kumamoto ◽

Michiko S Fujii

Keyword(s):

Open Cluster ◽

Formation Rate ◽

Open Clusters ◽

Type Star ◽

Dynamical Mechanism ◽

Milky Way Galaxy ◽

Triple Systems ◽

Stellar Collisions ◽

Solar Metallicity ◽

Helium Star

Abstract We estimate formation rates of LB-1-like systems through dynamical interactions in the framework of the theory of stellar evolution before the discovery of the LB-1 system. The LB-1 system contains a ∼70 ${M_{\odot}}$ black hole (BH), a so-called pair instability (PI) gap BH, and a B-type star with solar metallicity, and has nearly zero eccentricity. The most efficient formation mechanism is as follows. In an open cluster, a naked helium star (with ∼20 ${M_{\odot}}$) collides with a heavy main sequence star (with ∼50 ${M_{\odot}}$) which has a B-type companion. The collision results in a binary consisting of the collision product and the B-type star with a high eccentricity. The binary can be circularized through the dynamical tide with radiative damping of the collision product envelope. Finally, the collision product collapses to a PI-gap BH, avoiding pulsational pair instability and pair instability supernovae because its He core is as massive as the pre-colliding naked He star. We find that the number of LB-1-like systems in the Milky Way galaxy is ∼0.01(ρoc/104 ${M_{\odot}}$ pc−3), where ρoc is the initial mass densities of open clusters. If we take into account LB-1-like systems with O-type companion stars, the number increases to ∼0.03(ρoc/104 ${M_{\odot}}$ pc−3). This mechanism can form LB-1-like systems at least ten times more efficiently than the other mechanisms: captures of B-type stars by PI-gap BHs, stellar collisions between other types of stars, and stellar mergers in hierarchical triple systems. We conclude that no dynamical mechanism can explain the presence of the LB-1 system.

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