共查询到20条相似文献,搜索用时 31 毫秒
1.
S. V. Lapin 《Journal of Mathematical Sciences》2008,152(3):372-403
This paper is devoted to the introduction of a D
∞-differential analog of the notion of an E
∞-(co)algebra and to the construction of generalized Steenrod operations in terms of multiplicative spectral sequences. In
this paper, we investigate basic homotopy properties of D
∞-differential E
∞-(co)algebras and construct a spectral sequence of a D
∞-differential E
∞-(co)algebra.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology
and Its Applications, 2006. 相似文献
2.
Michael A. Mandell 《Publications Mathématiques de L'IHéS》2006,103(1):213-246
Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full. 相似文献
3.
Benoit Fresse 《Advances in Mathematics》2010,223(6):2049-2096
The standard reduced bar complex B(A) of a differential graded algebra A inherits a natural commutative algebra structure if A is a commutative algebra. We address an extension of this construction in the context of E-infinity algebras. We prove that the bar complex of any E-infinity algebra can be equipped with the structure of an E-infinity algebra so that the bar construction defines a functor from E-infinity algebras to E-infinity algebras. We prove the homotopy uniqueness of such natural E-infinity structures on the bar construction.We apply our construction to cochain complexes of topological spaces, which are instances of E-infinity algebras. We prove that the n-th iterated bar complexes of the cochain algebra of a space X is equivalent to the cochain complex of the n-fold iterated loop space of X, under reasonable connectedness, completeness and finiteness assumptions on X. 相似文献
4.
Mahmoud Benkhalifa 《Topology and its Applications》2008,155(12):1350-1370
The purpose of this paper is to classify the quasi-isomorphism classes of 1-connected minimal free cochain algebras over a commutative ring. Our tool to address this problem is a “certain” long sequence, called the Whitehead exact sequence, which we construct for every such algebra. We introduce the notion of coherent isomorphisms between these exact sequences and we show that two 1-connected minimal free cochain algebras are quasi-isomorphic if and only if their respective Whitehead exact sequences are coherently isomorphic. 相似文献
5.
Raymond Mortini 《Monatshefte für Mathematik》2011,36(4):299-311
We introduce the notion of generalized E-stable ranks for commutative unital Banach algebras and determine these ranks for the disk-algebra
A(\mathbbD){A(\mathbb{D})}, many of its subalgebras, and the algebra H
∞ of bounded holomorphic functions in the unit disk. Relations to L-sets and separating algebras, notions due to Csordas and Reiter, are given, too. Finally we show that the absolute stable
rank of
A(\mathbbD){A(\mathbb{D})} and H
∞ is bigger than 2. 相似文献
6.
R. Umble 《Journal of Mathematical Sciences》2008,152(3):443-450
We compute the structure relations in special A
∞-bialgebras whose operations are limited to those defining the underlying A
∞-(co)algebra substructure. Such bialgebras appear as the homology of certain loop spaces. Whereas structure relations in general
A
∞-bialgebras depend upon the combinatorics of permutahedra, only Stasheff’s associahedra are required here.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology
and Its Applications, 2006. 相似文献
7.
Pascal Lambrechts 《manuscripta mathematica》2000,103(2):143-160
A thickening of a finite CW-complex X is by definition a compact manifold M of the same simple homotopy type as X. We give a model for the cochain complex of the boundary of that manifold, C
*(δM), as a module over the cochain algebra C
*(X). We also show how to construct an algebraic model of the rational homotopy type of δC
*(M) from a model of X. Using this rational model, we prove a new formula for the rational Lusternik–Schnirelmann category of X.
Received: 24 September 1999 相似文献
8.
The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler is analyzed. Transitive irreducible
graded Lie algebras over an algebraically closed field of characteristic p > 2 with classical reductive component L
0 are considered. We show that if a nondegenerate Lie algebra L containes a transitive degenerate subalgebra L′such that dim L′1 > 1, then L is an infinite-dimensional Lie algebra.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 60, Algebra,
2008. 相似文献
9.
For a class of spaces including simply connected spaces and classifying spaces of nilpotent groups, relatively small differential graded algebras are constructed over commutative rings with 1 which are chain homotopy equivalent to the singular cochain algebra. An application to finitely generated torsion-free nilpotent groups over the integers is given. 相似文献
10.
On classifying monotone complete algebras of operators 总被引:1,自引:0,他引:1
We give a classification of “small” monotone complete C
*-algebras by order properties. We construct a corresponding semigroup. This classification filters out von Neumann algebras;
they are mapped to the zero of the classifying semigroup. We show that there are 2
c
distinct equivalence classes (where c is the cardinality of the continuum). This remains true when the classification is restricted to special classes of monotone
complete C
*-algebras e.g. factors, injective factors, injective operator systems and commutative algebras which are subalgebras of ℓ∞. Some examples and applications are given.
相似文献
11.
P. P. Nikitin 《Journal of Mathematical Sciences》2006,138(3):5727-5732
We consider the family of algebras {H
q
1,n
}
n=1
∞
, where H
q
1,n
is obtained by changing the first generator in the group algebra of the symmetric group Sn+1. We describe the irreducible representations of these algebras and construct the branching graph of the family {H
q
1,n
}
n=1
∞
. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 325, 2005, pp. 171–180. 相似文献
12.
Thomas Brüstle 《Compositio Mathematica》2001,129(3):301-323
In this note we classify the derived-tame tree algebras up to derived equivalence. A tree algebra is a basic algebra A = kQ/I whose quiver Q is a tree. The algebra A is said to be derived-tame when the repetitive category  of A is tame. We show that the tree algebra A is derived-tame precisely when its Euler form
A
is non-negative. Moreover, in this case, the derived equivalence class of A is determined by the following discrete invariants: The number of vertices, the corank and the Dynkin type of
A
. Representatives of these derived equivalence classes of algebras are given by the following algebras: the hereditary algebras of finite or tame type, the tubular algebras and a certain class of poset algebras, the so-called semichain-algebras which we introduce below. 相似文献
13.
We classify graph C
*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to
strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C
*-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence
of such algebras, without using the boundary operator algebra. A direct relation is given between the K
1-group of the algebra and the cycle space of the graph.
We thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K
0(
Ч) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University
College. 相似文献
14.
Alan Robinson 《Inventiones Mathematicae》2003,152(2):331-348
We prove that the stable homotopy of any Γ-module F is the homology of a bicomplex Ξ(F), in which the (q−1)st row is the two-sided bar construction ℬ(Lie*
q
,Σ
q
,F[q]). This gives a natural homotopical cotangent bicomplex for graded commutative algebras, in a form suitable for use in a
new obstruction theory for classifying E
∞ ring structures on spectra. The E
∞ structure on certain Lubin-Tate spectra is a corollary.
Oblatum 15-X-2001 & 14-X-2002?Published online: 24 February 2003 相似文献
15.
Let
\mathbbK{\mathbb{K}} be a field of characteristic p > 0 and S
1 the unit circle. We construct a model for the negative cylic homology of a commutative cochain algebra with two stages Sullivan
minimal model. Using the notion of shc-formality introduced in Bitjong and Thomas (Topology 41:85–106), the main result of Bitjong and El Haouari (Math Ann 338:347–354)
and techniques of Vigué-Poirrier (J Pure Appl Algebra 91:347–354) we compute the S
1-equivariant cohomology algebras of the free loop spaces of the infinite complex projective space
\mathbbCP(¥){\mathbb{CP}(\infty)} and the odd spheres S
2q+1. 相似文献
16.
Olga Bershtein 《Algebras and Representation Theory》2014,17(4):1083-1093
In this paper we study *-representations for polynomial algebras on quantum matrix spaces. We deal with two special cases of the polynomial algebras, namely the algebra of polynomials on quantum complex matrices Mat2 and on quantum complex symmetric matrices \(\mathrm{Mat_2^{sym}}\) . For the second algebra we classify all irreducible *-representations by bounded operators in a Hilbert space (up to a unitary equivalence). Moreover, we present a construction of *-representations of the above algebras which enables to obtain the full list of *-representations (sometimes by passing to subrepresentations). 相似文献
17.
Kenji Nishida 《Algebras and Representation Theory》2006,9(1):13-31
We generalize results of Foxby concerning a commutative Nötherian ring to a certain noncommutative Nötherian algebra Λ over a commutative Gorenstein complete local ring. We assume that Λ is a Cohen–Macaulay isolated singularity having a dualizing module. Then the same method as in the commutative cases works and we obtain a category equivalence between two subcategories of mod Λ, one of which includes all finitely generated modules of finite Gorenstein dimension. We give examples of such algebras which are not Gorenstien; orders related to almost Bass orders and some k-Gorenstein algebras for an integer k.Presented by I. Reiten
★The author is supported by Grant-in-Aid for Scientific Researches B(1) No. 14340007 in Japan. 相似文献
18.
Sergei A. Merkulov 《Bulletin of the Brazilian Mathematical Society》2011,42(4):683-781
We review several well-known operads of compactified configuration spaces and construct several new such operads, [`(C)]\bar C, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad
of A
∞-algebras and their homotopy morphisms, (ii) the 2-coloured operad of L
∞-algebras and their homotopy morphisms, and (iii) the 4-coloured operad of openclosed homotopy algebras and their homotopy
morphisms. Two gadgets — a (coloured) operad of Feynman graphs and a de Rham field theory on [`(C)]\bar C — are introduced and used to construct quantized representations of the (fundamental) chain operad of [`(C)]\bar C which are given by Feynman type sums over graphs and depend on choices of propagators. 相似文献
19.
Daniele Mundici 《Annals of Pure and Applied Logic》2011,162(12):1035-1047
We classify every finitely axiomatizable theory in infinite-valued propositional ?ukasiewicz logic by an abstract simplicial complex (V,Σ) equipped with a weight function ω:V→{1,2,…}. Using the W?odarczyk–Morelli solution of the weak Oda conjecture for toric varieties, we then construct a Turing computable one–one correspondence between (Alexander) equivalence classes of weighted abstract simplicial complexes, and equivalence classes of finitely axiomatizable theories, two theories being equivalent if their Lindenbaum algebras are isomorphic. We discuss the relationship between our classification and Markov’s undecidability theorem for PL-homeomorphism of rational polyhedra. 相似文献
20.
A Poisson algebra is a Lie algebra endowed with a commutative associative product in such a way that the Lie and associative products are compatible via a Leibniz rule. If we part from a Lie color algebra, instead of a Lie algebra, a graded-commutative associative product and a graded-version Leibniz rule we get a so-called Poisson color algebra (of degree zero). This concept can be extended to any degree, so as to obtain the class of Poisson color algebras of arbitrary degree. This class turns out to be a wide class of algebras containing the ones of Lie color algebras (and so Lie superalgebras and Lie algebras), Poisson algebras, graded Poisson algebras, z-Poisson algebras, Gerstenhaber algebras, and Schouten algebras among other classes of algebras. The present paper is devoted to the study of structure of Poisson color algebras of degree g0, where g0 is some element of the grading group G such that g0 = 0 or 4g0≠0, and with restrictions neither on the dimension nor the base field, by stating a second Wedderburn-type theorem for this class of algebras. 相似文献