Introducing products between multivectors of Cl0,7 (the Clifford algebra over the metric vector space R) and octonions, resulting in an octonion, and leading to the non-associative standard octonionic product in a particular case, we generalize the octonionic X-product, associated with the transformation rules for bosonic and fermionic fields on the tangent bundle over the 7-sphere S, and the X...

The structure of arbitrary associative commutative unital artinian algebras is well-known: they are finite products of associative commutative unital local algebras [6, pg.351, Cor. 23.12]. In the semi-simple case, we have the Artin-Wedderburn Theorem which states that any semi-simple artinian algebra (which is assumed to be associative and unital but not necessarily commutative) is a direct pr...

Binary Constraint Problems have traditionally been considered as Network Satisfaction Problems over some relation algebra. A constraint network is satisfiable if its nodes can be mapped into some representation of the relation algebra in such a way that the constraints are preserved. A qualitative representation φ is like an ordinary representation, but instead of requiring (a ; b) = a | b, as ...

Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that, if KG is Lie nilpotent, then its upper (or lower) Lie nilpotency index is at most |G| + 1, where |G| is the order of the commutator subgroup. Previously we determined the groups G for which the upper/lower nilpotency index is maximal or the upper nilpotency index is ‘almost maximal’ (that is, ...

A current Lie algebra is contructed from a tensor product of a Lie algebra and a commutative associative algebra of dimension greater than 2. In this work we are interested in deformations of such algebras and in the problem of rigidity. In particular we prove that a current Lie algebra is rigid if it is isomorphic to a direct product g× g × ...× g where g is a rigid Lie algebra. 1 Current Lie ...

We consider a non-associative generalization of MV-algebras. The underlying posets of our non-associative MV-algebras are not lattices, but they are related to so-called λ-lattices. c ©2007 Mathematical Institute Slovak Academy of Sciences 1. Non-associative MV-algebras As known, MV-algebras were introduced in the late-fifties by C . C . C h a n g as an algebraic semantics of the Lukasiewicz ma...

We prove that an associative algebra A is isomorphic to a subalgebra of a C∗-algebra if and only if its ∗-double A∗A∗ is ∗-isomorphic to a ∗-subalgebra of a C∗-algebra. In particular each operator algebra is shown to be completely boundedly isomorphic to an operator algebra B with the greatest C∗-subalgebra consisting of the multiples of the unit and such that each element in B is determined by...

We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve the equation of deformations in a polynomial frame. We consider also the deformations of the enveloping algebra of a rigid Lie algebra and we define valued de...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...