Triple Derivations and Triple Homomorphisms of Perfect Lie Superalgebras

In this paper, we study triple derivations and triple homomorphisms of perfect Lie superalgebras over a commutative ring $R$. It is proved that, if the base ring contains $\frac{1}{2}$, $L$ is a perfect Lie superalgebra with zero center, then every triple derivation of $L$ is a derivation, and every triple derivation of the derivation algebra $Der (L)$ is an inner derivation. Let $L,~L^{'}$ be Lie superalgebras over a commutative ring $R$, the notion of triple homomorphism from $L$ to $L^{'}$ is introduced. We proved that, under certain assumptions, homomorphisms, anti-homomorphisms, and sums of homomorphisms and anti-homomorphisms are all triple homomorphisms.Comment: 12pages in Indagationes Mathematicae, 201

Common Origin of (-)^L, (-)^{3B}, and Strong CP Conservation

The multiplicative conservation of both lepton and baryon numbers, i.e. (-)^L and (-)^{3B}, is connected to an axionic solution of the strong CP problem in a supersymmetric, unifiable model of quark and lepton interactions. New particles are predicted at the TeV scale, with verifiable consequences at the Large Hadron Collider.Comment: 9 pages, no figur

Derivation of Dark Matter Parity from Lepton Parity

It is shown that in extensions of the standard model of quarks and leptons where additive lepton number $L$ is broken by two units, so that $Z_2$ lepton parity, i.e. $(-1)^L$ which is either even or odd, remains exactly conserved, there is the possibility of stable dark matter without additional symmetry. This applies to many existing simple models of Majorana neutrino mass with dark matter, including some radiative models. Several well-known examples are discussed. This new insight leads to the construction of a radiative Type II seesaw model of neutrino mass with dark matter where the dominant decay of the doubly charged Higgs boson $\xi^{++}$ is into $W^+W^+$ instead of the expected $l_i^+ l_j^+$ lepton pairs for the well-known tree-level model.Comment: 11 pages, 6 figures, version to appear in PR

Hymn to the heroes of Malta

Ġabra ta’ poeżiji u proża li tinkludi: Alla fil-ħolqien ta’ Ġużè Agius Bonello – Is-sena u l-bniedem ta’ Ġużè Ellul-Mercer – Li tiżra’ taħsad ta’ Vic. Apap – Huwa ta’ Gino Muscat-Azzopardi – Żewġ friefet ta’ Vincent Caruana – Iċ-ċagħka ta’ Ġużè Borg – Warda midbiela ta’ C. Gauci – It-tfajla tas-sulfarini ta’ Albert M. Cassola – L-aħħar traduzzjoni ta’ May Butcher qabel ma mietet – Hymn to the heroes of Malta.N/

Hogyan írjunk ma mongol történelmet?

Dendew, L.: Mongoliin towč tüüx [Mongólia rövid története]. Ulaanbaatar: Monsudar 2012

Tlett mudelli ta' direttur haddiem

Jiena qatt ma kont haddiem direttur u allura zgur li ma nistax nitkellem minn esperjenza. Pero forsi dak huwa il-vantagg tieghi illum. Il-kuncett ta' direttur haddiem huwa diga kontradizzjoni fIh nifsu. Jien ghalija haddiem, direttur, x'int int? Diga qed tilbes zewgt ikpiepel. Din hija wahda mill-problemi bhala haddiem direttur. Inhobbu nghidu: liema direttur? Huma bhal diretturi ohra?Ghandhom l-istess responsabilitajiet? l-istess poteri? Ikollhom l-istess drittijiet? Imma skuzi mhumiex bhad-diretturi l-ohra u ma jistghux ikunu bhad-diretturi ohra ghax id-diretturi l-ohra ma jahdmux fl-istess post tax-xoghol. Diga hemm dan l-aspett partikolari. Huwa mportanti li niftakru li jekk inti ghandek persuna li tahdem f'dak il-post tax-xoghol din diga ghandha nteress differenti.peer-reviewe