Generalizations of the series exp and log to noncommutative non-associative and other types of algebras were regarded by M. Lazard, and recently by V. Drensky and L. Gerritzen. There is a unique power series exp(x) in one non-associative variable x such that exp(x) exp(x) = exp(2x), exp ′ (0) = 1. We call the unique series H = H(x, y) in two non-associative variables satisfying exp(H) = exp(x) ...

Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra A together with a Lie algebra L mapped into the derivations of A. A bicomplex (with both Hochschild and Chevalley-Eilenberg cohomologies) is essential. The importance of Poisson algebras in classical mechanics makes it useful to have a...

Abstract. Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = lim sup n→∞ n √ an, where an is the vector space dimension of the n’th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) ≤ √ a2. Using some results of Friedland on the maximal spectral radius of (0, 1)-matrices wit...

For the associative algebra A(g) of an infinite-dimensional Lie g, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers such are given by elements algebraic completion space formal series in complex parameters, sections provided rational functions with prescribed analytic properties. Homotopical invariance as well covariance terms trivial A(g)-bundles is proven. ...

A proof that the prepotential for pure N=2 Super-Yang-Mills theory associated with Lie algebras Br and Cr satisfies the generalized WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) system was given by Marshakov, Mironov and Morozov. Among other things, they use an associative algebra of holomorphic differentials. Later Ito and Yang used a different approach to try to accomplish the same result, but th...

Lattice associative memories also known as morphological associative memories are fully connected feedforward neural networks with no hidden layers, whose computation at each node is carried out with lattice algebra operations. These networks are a relatively recent development in the field of associative memories that has proven to be an alternative way to work with sets of pattern pairs for w...

A method for the construction of classes examples multi-dimensional, multi-component Dubrovin-Novikov brackets hydrodynamic type is given. This based on an extension original Gelfand and Dorfman which gave Novikov algebras in terms structures defined from commutative, associative algebras. Given such algebra, involves only linear algebra.