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51.
52.
A. Van Daele 《代数通讯》2013,41(6):2341-2386
A simple and nice structure theorem for orthogroups was given by Petrich in 1987. In this paper, we consider a generalized orthogroup, that is, a quasi-completely regular semigroup with a band of idempotents in which its set of regular elements, namely, RegS, forms an ideal of S. A method of construction of such semigroups is provided and as a result, the Petrich structure theorem of orthogroups becomes an immediate corollary of our theorem on generalized orthogroups. An example of such generalized orthogroup is also constructed. This example provides some useful information for the construction of various kinds of quasi-completely regular semigroups. 相似文献
53.
kevin J. Carlin 《代数通讯》2013,41(1):1-13
A fundamental approach to the homological algebra of rational modules in positive characteristic p should begin with the translation properties of injective modules. This point of view leads to the study of functors related to coherent translation and their effect on the injective indecomposable modules indexed by p-regular dominant weights. The main result shows that the calculation can often be reduced to a corresponding calculation on the principal indecomposable modules of the Frobenius kernel. 1 相似文献
54.
《Journal of Pure and Applied Algebra》2022,226(8):107018
We study the algebraic K-theory and Grothendieck–Witt theory of proto-exact categories, with a particular focus on classes of examples of -linear nature. Our main results are analogues of theorems of Quillen and Schlichting, relating the K-theory or Grothendieck–Witt theory spaces of proto-exact categories defined using the (hermitian) Q-construction and group completion. 相似文献
55.
We leverage the results of the prequel [8], in combination with a theorem of D. Orlov to create a categorical covering picture for factorizations. As applications, we provide a conjectural geometric framework to further understand M. Kontsevich's Homological Mirror Symmetry conjecture and obtain new cases of a conjecture of Orlov concerning the Rouquier dimension of the bounded derived category of coherent sheaves on a smooth variety. 相似文献
56.
Marco Grandis 《Applied Categorical Structures》1997,5(1):75-97
We study here a notion of simplicial satellites, as a first step towards a characterisation of simplicial derived functors, a problem unsolved since the latter were introduced.The problem comes from the fact that, in contrast with the abelian case, simplicial derived functors do not produce by themselves an exact sequence. Our solution consists in extending them to commutative k-cubes, for all k, forming thus an exact system of functors universal within the connected ones; or, in other words, a system of simplicial satellites. The tool we develop here for this extension is the homotopy kernel of a commutative k-dimensional cubic diagram, generalising the homotopy kernel of a map; its 2-dimensional version has already been proved essential in other homotopical topics. 相似文献
57.
Gábor Elek 《K-Theory》1998,13(1):1-22
We prove that, for any exact category M, any element of K1(M)can be described in terms of a pair of admissible monomorphisms A X, B Y and an isomorphism :A X/A Y B Y/B X. 相似文献
58.
We equip the category
of linear maps of vector spaces with a tensor product which makes it suitable for various constructions related to Leibniz algebras. In particular, a Leibniz algebra becomes a Lie object in
and the universal enveloping algebra functor UL from Leibniz algebras to associative algebras factors through the category of cocommutative Hopf algebras in
. This enables us to prove a Milnor-Moore type theorem for Leibniz algebras. 相似文献
59.
Chen Jixiang 《数学学报(英文版)》1998,14(3):321-326
K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH
B
over a fixed spaceB ([1]). They have introduced two pairs of adjoint functors:P
B
N
B
andm
*
m
*, whereP
B
:H
B
→H
B
, andm
*:H
A
→H
B
for a fixed mapm:A→B. We have introduced a split fibration of categoriesL:H
b
→H
B
and provedL
J, J
L in [2]. This paper first extendsP
B
N
B
to
for any fixed mapb:
. Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categoriesH
b
andH
b
whereH
b
is the dual ofH
b
. One of our results isN
b
P
b
. This differs fromP
B
N
B
.
Supported by National Natural Science Foundation of China 相似文献
60.
Olaf Berndt 《Applied Categorical Structures》1998,6(1):37-62
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 of commutative Banach algebras and locally compact topological groups, and semidirect sums of compact Hausdorff spaces with basepoint. Also, further applications to commutative Banach algebras are given. 相似文献