Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

We analyse super non-Abelian T-duality for principal chiral models, symmetric space sigma and semi-symmetric models general Lie supergroups. This includes along both bosonic fermionic directions. As an example, we perform the explicit dualisation of OSp(1|2) model, and, whilst target superspace this model is a three-dimensional supergravity background, find that its T-dual falls outside class s...

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current jμ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. University of Freiburg THEP 91/10 August 1991 ∗Address after September 1, 1991: Department of Mathemati...

In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid pattern $p$ $\Delta$ if there no factor $f$ of such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ non-erasing morphism. A be $k$-avoidable exists infinite $k$-letter avoids $p$. \emph{doubled} every variable occurs at least twice. Doubled patterns are known $3$-avoidable. Currie, Mol, and Rampersad have considered ge...

In ‎this ‎paper, ‎we ‎study ‎the ‎relation ‎between ‎the ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎with ‎the ‎lattice theory. ‎We ‎introduce ‎the ‎concepts ‎of ‎the ‎lattice ‎of ‎soft ‎sets, ‎full ‎soft ‎sets ‎and ‎soft ‎Lie ‎algebras ‎and next, we ‎verify ‎some ‎properties ‎of ‎them. We ‎prove ‎that ‎the ‎lattice ‎of ‎the ‎soft ‎sets ‎on ‎a fixed parameter set is isomorphic to the power set of a ...

Starting from the classification of 6–dimensional real Drinfeld doubles and their decomposition into Manin triples we construct 3–dimensional Poisson–Lie T–dual or more precisely T–plural sigma models. Of special interest are those that are conformally invariant. Examples of models that satisfy vanishing β–function equations with zero dilaton are presented and their duals are calculated. It tur...

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...