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For any punctured category , a definition of a ‘ semidirect product ’ and its dual counterpart, a ‘ semidirect sum’, is given. Several examples are studied, among which are semidirect products ...
We give an algebraic characterization, based on the bilateral semidirect product of finite monoids, of the quantifier alternation hierarchy in two-variable first-order logic on finite words ...
\(\mathbf {Ab}_p\) is the pseudovariety of all elementary abelian p-groups and \(\mathbf {J}*\mathbf {Ab}_p\) is the pseudovariety of monoids generated by the class of all semidirect products of monoids from ...
-dual. As an application , the degenerate Sklyanin algebra is shown to be isomorphic to the braided matricesBM q(2); it is a braided-commutative bialgebra in a braided category . As a second application , we ...
representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincaré groups in arbitrary dimension and signature. Finally we compare our results with those ...
in two different ways: Firstly we construct the coproduct M ᴼ* N by using the free product M * N of pre-R-algebroids M and N, and then we construct the coproduct M ᴼ⋉ N by using the semidirect product M ...
group in the usual sense, then the semidirect product F := G n V of G and V is a Lie group and at the same time a vector bundle over G such that both structures are compatible in the following sense: ...
FINITE-DIMENSIONAL REPRESENTATIONS OF THE LIE ALGEBRA sl2~R ~ R. S. Ismagilov UDC 519.46 Let L be the Lie algebra of real matrices d , a--~ d = O; (i 0 i) it is identified with the semidirect ...
and a simple unital AF-algebra whose central sequences are all trivial. This concludes that even for approximately finite-dimensional algebras, in the non-separable category , the tensor product structure ...
be given in the category Grp of groups. Let N ◁ G be any normal subgroup of G and form the semidirect product G × N having as elements the pairs for x ∈ G, n ∈ N with the (associative) multiplication ...
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