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1.
Let H be a Hopf π-coalgebra over a commutative ring k with bijective antipode S, and A and B right π-H-comodulelike algebras. We show that the pair of adjoint functors (F3 = A Bop A□ HBop -,G3 = (-)coH) between the categories A□HBopM and AMπB-H is a pair of inverse equivalences, when A is a faithfully flat π-H-Galois extension. Furthermore, the categories Moritaπ-H(A,B) and Morita □π-H(AcoH,BcoH) are equivalent, if A and B are faithfully flat π-H-Galois extensions. 相似文献
2.
Christopher Kennedy 《Algebras and Representation Theory》2011,14(6):1187-1202
This paper continues the study of associative and Lie deep matrix algebras,
DM(X,\mathbbK){\mathcal{DM}}(X,{\mathbb{K}}) and
\mathfrakgld(X,\mathbbK){\mathfrak{gld}}(X,{\mathbb{K}}), and their subalgebras. After a brief overview of the general construction, balanced deep matrix subalgebras,
BDM(X,\mathbbK){\mathcal{BDM}}(X,{\mathbb{K}}) and
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}), are defined and studied for an infinite set X. The global structures of these two algebras are studied, devising a depth grading on both as well as determining their ideal
lattices. In particular,
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) is shown to be semisimple. The Lie algebra
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) possesses a deep Cartan decomposition and is locally finite with every finite subalgebra naturally enveloped by a semi-direct
product of
\mathfraksln{\mathfrak{{sl}_n}}’s. We classify all associative bilinear forms on
\mathfraksl2\mathfrakd{\mathfrak{sl}_2\mathfrak{d}} (a natural depth analogue of
\mathfraksl2{\mathfrak{{sl}_2}}) and
\mathfrakbld{\mathfrak{bld}}. 相似文献
3.
To each irreducible infinite dimensional representation $(\pi ,\mathcal {H})$ of a C*‐algebra $\mathcal {A}$, we associate a collection of irreducible norm‐continuous unitary representations $\pi _{\lambda }^\mathcal {A}$ of its unitary group ${\rm U}(\mathcal {A})$, whose equivalence classes are parameterized by highest weights in the same way as the irreducible bounded unitary representations of the group ${\rm U}_\infty (\mathcal {H}) = {\rm U}(\mathcal {H}) \cap (\mathbf {1} + K(\mathcal {H}))$ are. These are precisely the representations arising in the decomposition of the tensor products $\mathcal {H}^{\otimes n} \otimes (\mathcal {H}^*)^{\otimes m}$ under ${\rm U}(\mathcal {A})$. We show that these representations can be realized by sections of holomorphic line bundles over homogeneous Kähler manifolds on which ${\rm U}(\mathcal {A})$ acts transitively and that the corresponding norm‐closed momentum sets $I_{\pi _\lambda ^\mathcal {A}}^{\bf n} \subseteq {\mathfrak u}(\mathcal {A})^{\prime }$ distinguish inequivalent representations of this type. 相似文献
4.
5.
给出了3-李代数的广义导子、拟导子、拟型心的定义,研究了他们之间的结构关系,并对具有极大对角环面的3-李代数的拟导子和拟型心结构进行了系统的研究.证明了(1)广义导代数GDer(A)可以分解成拟导子代数QDer(A)和拟型心QΓ(A)的直和;(2)3-李代数A的拟导子可以扩张成一个具有较大维数的3-李代数的导子;(3)拟导子代数QDer(A)包含在拟型心的正规化子中,表示为[QDer(A),QΓ(A)]?QΓ(A);(4)如果A包含极大对角环面T,那么QDer(A)和Qr(A)是T的对角模,也就是(T,T)半单地作用在QDer(A)和QΓ(A)上. 相似文献
6.
H. Zöschinger 《Archiv der Mathematik》2003,81(2):126-141
Suppose that $(R, m)$ is a noetherian local ring and that E is the
injective hull of the residue class field $R/m$. Suppose that M is an
R-module, $M^0 = {\mbox{\rm Hom}}_R (M, E)$ is the Matlis dual of
M and ${\mbox{\rm Coass}(M)} = {\mbox{\rm Ass} (M^0)}$. M is
called cotorsion if every prime ideal ${\frak p} \in {\mbox{\rm Coass}}(M)$ is
regular; it is called strongly cotorsion if $\cap {\rm Coass}(M)$ is regular.
In the first part, we completely describe the structure of the strongly
cotorsion modules over R, use this to determine the coassociated prime
ideals of the bidual $M^{00}$, and give in the second part
criteria for a cotorsion module being strongly cotorsion.
Received: 7 March 2002 相似文献
7.
In this paper, we study the properties of generalized power series modules and the filtration dimensions of generalized power series algebras. We obtain that [[△S,≤]]- gfd([[AS,≤]]) =△-gfd(A) if A is an R-module where R is a perfect and coherent commutative algebra, and(R, ≤) is standardly stratified. 相似文献
8.
9.
Let F be a field of characteristic 0, Mn(F) the full matrix algebra over F, t the subalgebra of Mn(F) consisting of all upper triangular matrices. Any subalgebra of Mn(F) containing t is called a parabolic subalgebra of Mn(F). Let P be a parabolic subalgebra of Mn(F). A map φ on P is said to satisfy derivability if φ(x·y) = φ(x)·y+x·φ(y) for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn(F) is an inner derivation. 相似文献
10.
A deeper understanding of recent computations of the Brauer group of Hopf algebras is attained by explaining why a direct product decomposition for this group holds and describing the non-interpreted factor occurring in it. For a Hopf algebra B in a braided monoidal category ${{\mathcal C}}$ , and under certain assumptions on the braiding (fulfilled if ${{\mathcal C}}$ is symmetric), we construct a sequence for the Brauer group ${{\rm{BM}}}({{\mathcal C}};B)$ of B-module algebras, generalizing Beattie’s one. It allows one to prove that ${{\rm{BM}}}({{\mathcal C}};B) \cong {{\rm{Br}}}({{\mathcal C}}) \times {\operatorname{Gal}}({{\mathcal C}};B)$ , where ${{\rm{Br}}}({{\mathcal C}})$ is the Brauer group of ${{\mathcal C}}$ and ${\operatorname{Gal}}({{\mathcal C}};B)$ the group of B-Galois objects. We also show that ${{\rm{BM}}}({{\mathcal C}};B)$ contains a subgroup isomorphic to ${{\rm{Br}}}({{\mathcal C}}) \times {\operatorname{H^2}}({{\mathcal C}};B,I),$ where ${\operatorname{H^2}}({{\mathcal C}};B,I)$ is the second Sweedler cohomology group of B with values in the unit object I of ${{\mathcal C}}$ . These results are applied to the Brauer group ${{\rm{BM}}}(K,B \times H,{{\mathcal R}})$ of a quasi-triangular Hopf algebra that is a Radford biproduct B × H, where H is a usual Hopf algebra over a field K, the Hopf subalgebra generated by the quasi-triangular structure ${{\mathcal R}}$ is contained in H and B is a Hopf algebra in the category ${}_H{{\mathcal M}}$ of left H-modules. The Hopf algebras whose Brauer group was recently computed fit this framework. We finally show that ${{\rm{BM}}}(K,H,{{\mathcal R}}) \times {\operatorname{H^2}}({}_H{{\mathcal M}};B,K)$ is a subgroup of ${{\rm{BM}}}(K,B \times H,{{\mathcal R}})$ , confirming the suspicion that a certain cohomology group of B × H (second lazy cohomology group was conjectured) embeds into it. New examples of Brauer groups of quasi-triangular Hopf algebras are computed using this sequence. 相似文献
11.
We develop structural formulas
satisfied by some families of
orthogonal matrix polynomials of size $2\times 2$ satisfying
second-order differential equations with polynomial coefficients. We consider
here two one-parametric families of weight matrices,
namely
\[
H_{a,1}(t)\;=\;e^{-t^2} \left( \begin{array}{@{}cc@{}}
1+\vert a\vert ^2t^2 & at \\bar at & 1 \end{array} \right) \quad {\rm and} \quad H_{a,2}(t)\;=\;e^{-t^2} \left( \begin{array} {@{}cc@{}}
1+\vert a\vert ^2t^4 & at^2 \\bar at^2 & 1
\end{array} \right),
\]
$a\in \mbox{\bf C} $ and $t\in \mbox{\bf R} $, and their corresponding orthogonal
polynomials. 相似文献
12.
Zhixiang Wu 《Acta Appl Math》2009,106(2):185-198
In present paper we define a new kind of weak quantized enveloping algebra
of Borcherds superalgebras
. It is a noncommutative and noncocommutative weak graded Hopf algebra. Using localizing with some Ore set, we obtain a different
kind of quantized enveloping algebras of Borcherds superalgebras
. It has a homomorphic image which is isomorphic to the usual quantum enveloping algebra
of
. Moreover,
is isomorphic to a direct sum of
and an other algebra as algebras.
The author is sponsored by ZJNSF No. Y607136. 相似文献
13.
Dániel Gerbner Nathan Lemons Cory Palmer Dömötör Pálvölgyi Balázs Patkós Vajk Szécsi 《Graphs and Combinatorics》2013,29(3):489-498
For a set G and a family of sets ${\mathcal{F}}$ let ${\mathcal{D}_{\mathcal{F}}(G)=\{F\in \mathcal{F}:F\cap G=\emptyset\}}$ and ${\mathcal{S}_{\mathcal{F}}(G)=\{F\in\mathcal{F}:F\subseteq G\,{\rm or} \,G \subseteq F\}.}$ We say that a family is l-almost intersecting, (≤ l)-almost intersecting, l-almost Sperner, (≤ l)-almost Sperner if ${|\mathcal{D}_{\mathcal{F}}(F)|=l, |\mathcal{D}_{\mathcal{F}}(F)|\le l, |\mathcal{S}_{\mathcal{F}}(F)|=l, |\mathcal{S}_{\mathcal{F}}(F)| \le l}$ (respectively) for all ${F \in \mathcal{F}.}$ We consider the problem of finding the largest possible family for each of the above properties. We also address the analogous generalization of cross-intersecting and cross-Sperner families. 相似文献
14.
15.
Valentijn Karemaker 《Archiv der Mathematik》2016,107(4):341-353
We study the local Hecke algebra \({\mathcal{H}_{G}(K)}\) for \({G = {\rm GL}_{n}}\) and K a non-archimedean local field of characteristic zero. We show that for \({G = {\rm GL}_{2}}\) and any two such fields K and L, there is a Morita equivalence \({\mathcal{H}_{G}(K) \sim_{M} \mathcal{H}_{G}(L)}\), by using the Bernstein decomposition of the Hecke algebra and determining the intertwining algebras that yield the Bernstein blocks up to Morita equivalence. By contrast, we prove that for \({G = {\rm GL}_{n}}\), there is an algebra isomorphism \({\mathcal{H}_{G}(K) \cong \mathcal{H}_{G}(L)}\) which is an isometry for the induced \({L^1}\)-norm if and only if there is a field isomorphism \({K \cong L}\). 相似文献
16.
We discuss the notion of characteristic Lie algebra of a hyperbolic PDE. The integrability of a hyperbolic PDE is closely related to the properties of the corresponding characteristic Lie algebra χ. We establish two explicit isomorphisms:
Hence the Lie algebras \(\chi (\sinh {u})\) and χ(eu + e??2u) are slowly linearly growing Lie algebras with average growth rates \(\frac {3}{2}\) and \(\frac {4}{3}\) respectively. 相似文献
- 1)the first one is between the characteristic Lie algebra \(\chi (\sinh {u})\) of the sinh-Gordon equation \(u_{xy}=\sinh {u}\) and the non-negative part \({\mathcal {L}}({\mathfrak {sl}}(2,{\mathbb {C}}))^{\ge 0}\) of the loop algebra of \({\mathfrak {sl}}(2,{\mathbb {C}})\) that corresponds to the Kac-Moody algebra \(A_{1}^{(1)}\)$$\chi(\sinh{u})\cong {\mathcal{L}}({\mathfrak{s}\mathfrak{l}}(2,{\mathbb{C}}))^{\ge 0}={\mathfrak{s}\mathfrak{l}}(2, {\mathbb{C}}) \otimes {\mathbb{C}}[t]. $$
- 2)the second isomorphism is for the Tzitzeica equation uxy = eu + e??2uwhere \({\mathcal {L}}({\mathfrak {sl}}(3,{\mathbb {C}}), \mu )=\bigoplus _{j \in {\mathbb {Z}}}{\mathfrak {g}}_{j (\text {mod} \; 2)} \otimes t^{j}\) is the twisted loop algebra of the simple Lie algebra \({\mathfrak {sl}}(3,{\mathbb {C}})\) that corresponds to the Kac-Moody algebra \(A_{2}^{(2)}\).$$\chi(e^{u}{+}e^{-2u}) \cong {\mathcal{L}}({\mathfrak{s}\mathfrak{l}}(3,{\mathbb{C}}), \mu)^{\ge0}=\bigoplus_{j = 0}^{+\infty}{\mathfrak{g}}_{j (\text{mod} \; 2)} \otimes t^{j}, $$
17.
Etienne Desquith 《Proceedings of the American Mathematical Society》2003,131(7):2109-2119
Given a Banach algebra , R. Larsen defined, in his book ``An introduction to the theory of multipliers", a Banach algebra by means of a multiplier on , and essentially used it in the case of a commutative semisimple Banach algebra to prove a result on multiplications which preserve regular maximal ideals. Here, we consider the analogue Banach algebra induced by a bounded double centralizer of a Banach algebra . Then, our main concern is devoted to the relationships between , , and the algebras of bounded double centralizers and of and , respectively. By removing the assumption of semisimplicity, we generalize some results proven by Larsen.
18.
Thomas Kuhn Hans-Gerd Leopold Winfried Sickel Leszek Skrzypczak 《Constructive Approximation》2005,23(1):61-77
We investigate the asymptotic behavior of the entropy numbers of the
compact embedding
$$
B^{s_1}_{p_1,q_1} \!\!(\mbox{\footnotesize\bf R}^d, \alpha) \hookrightarrow B^{s_2}_{p_2,q_2} \!\!({\xxR}).
$$
Here $B^s_{p,q} \!({\mbox{\footnotesize\bf R}^d}, \alpha)$ denotes a weighted Besov space, where the weight is
given by $w_\alpha (x) = (1+| x |^2)^{\alpha/2}$, and
$B^{s_2}_{p_2,q_2} \!({\mbox{\footnotesize\bf R}^d})$ denotes the unweighted Besov space, respectively.
We shall concentrate
on the so-called limiting situation given by the following constellation of
parameters: $s_2 < s_1$, $0 < p_1,p_2 \le \infty$, and
$$
\alpha = s_1 - \frac{d}{p_1} - s_2 + \frac{d}{p_2} >
d \, \max \Big(0, \frac{1}{p_2}-\frac{1}{p_1}\Big).
$$
In almost all cases we give a sharp two-sided estimate. 相似文献
19.
Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ :A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies (A - B)R = R(A-B) ξR ((A-B)→ (φ(B))φ(R) =φ(R)((A)- (B)) for A, B, R E .4 and for some scalar 相似文献
20.
We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show∑that such a split regular Hom-Poisson color algebras A is of the form A = U +αIα with U a subspace of a maximal abelian subalgebra H and any Iα, a well described ideal of A, satisfying[Iα, Iβ] + IαIβ = 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized. 相似文献