3 citations · 8 across the 7 of their papers we have counts for
8 papers
The loop of formal power series with noncommutative coefficients under substitution
José M. Pérez-Izquierdo
The set of formal power series with coefficients in an associative but noncommutative algebra becomes a loop with the substitution product. We initiate the study of this loop by de…
On torsion-free nilpotent loops
J. Mostovoy, J. M. Perez-Izquierdo, I. P. Shestakov
We show that a torsion-free nilpotent loop (that is, a loop nilpotent with respect to the dimension filtration) has a torsion-free nilpotent left multiplication group of, at most,…
A Non-associative Baker-Campbell-Hausdorff formula
J. Mostovoy, J. M. Perez-Izquierdo, I. P. Shestakov
We address the problem of constructing the non-associative version of the Dynkin form of the Baker-Campbell-Hausdorff formula; that is, expressing , where $…
Co-Moufang deformations of the universal enveloping algebra of the algebra of traceless octonions
José M. Pérez-Izquierdo, I. P. Shestakov
By means of graphical calculus we prove that, over fields of characteristic zero, any bialgebra deformation of the universal enveloping algebra of the algebra of traceless octonion…
Nilpotent Sabinin algebras
J. Mostovoy, J. M. Perez-Izquierdo, I. P. Shestakov
In this note we establish several basic properties of nilpotent Sabinin algebras. Namely, we show that nilpotent Sabinin algebras (1) can be integrated to produce nilpotent loops,…
Hopf algebras in non-associative Lie theory
J. Mostovoy, J. M. Pérez-Izquierdo, I. P. Shestakov
We review the developments in the Lie theory for non-associative products from 2000 to date and describe the current understanding of the subject in view of the recent works, many…
Formal multiplications, bialgebras of distributions and non-associative Lie theory
J. Mostovoy, J. M. Pérez-Izquierdo
We describe the general non-associative version of Lie theory that relates unital formal multiplications (formal loops), Sabinin algebras and non-associative bialgebras. Starting w…
Dimension filtration on loops
J. Mostovoy, J. M. Pérez-Izquierdo
We show that the graded group associated to the dimension filtration on a loop acquires the structure of a Sabinin algebra after being tensored with a field of characteristic zero.…