Group graded Morita equivalences for wreath products
Virgilius-Aurelian Minuta
本文从群分次Morita等价出发，构造了张量积与圈积的Morita等价，推广了相关理论。
从群分次Morita等价出发，我们获得了张量积和圈积的Morita等价。
Starting with group graded Morita equivalences, we obtain Morita equivalences for tensor products and wreath products.
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Graded Morita theory over a G-graded G-acted algebra
针对有限群G，在G-分次G-作用代数上建立了群分次Morita理论。
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This note uses a variation of graded Morita theory for finite dimensional superalgebras to determine explicitly the graded basic superalgebras for all real and complex Clifford superalgebras. As an application, the Grothendieck groups of the category of left $\mathbb{Z}_2$-graded modules over all real and complex Clifford superalgebras are described explicitly.
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We study the structural and homological properties of graded Artinian modules over generalized Weyl algebras (GWAs), and this leads to a decomposition result for the category of graded Artinian modules. Then we define and examine a category of graded modules analogous to the BGG category O. We discover a condition on the data defining the GWA that ensures O has a system of projective generators. Under this condition, O has nice representation-theoretic properties. There is also a decomposition result for O. Next, we give a necessary condition for there to be a strongly graded Morita equivalenc…
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In this paper, we present a method to construct new stable equivalences of Morita type. Suppose that a stable equivalence of Morita type between finite dimensional algebras $A$ and $B$ is defined by a $B$-$A$-bimodule $N$. Then, for any finite admissible set $Φ$ of natural numbers and any generator $X$ of the $A$-module category, the $Φ$-Beilinson-Green algebras $\scr G^Φ_A(X)$ and $\scr G^Φ_B(N\otimes_AX)$ are stably equivalent of Morita type. In particular, if $Φ=\{0\}$, we get a known result in literature. As another consequence, we construct an infinite family of derived equivalent algebra…
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To a finite group G one can associate a tower of wreath products S_n[G]. It is well known that the graded direct sum of the Grothendieck groups of the categories of finite dimensional complex representations of these groups can be given the structure of a graded Hopf algebra, and in fact a positive self-adjoint Hopf algebra in the sense of Zelevinsky [1], using the induction product and restriction coproduct. This paper introduces and explores an analogously defined algebra/coalgebra structure associated to a more general class of towers of groups, obtained as a certain family of subgroups of …
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We give a sufficient condition for the $kG$-Scott module with vertex $P$ to remain indecomposable under taking the Brauer construction for any subgroup $Q$ of $P$ as $k[Q\,C_G(Q)]$-module, where $k$ is a field of characteristic $2$, and $P$ is a wreathed $2$-subgroup of a finite group $G$. This generalizes results for the cases where $P$ is abelian and some others. The motivation of this paper is that the Brauer indecomposability of a $p$-permutation bimodule ($p$ is a prime) is one of the key steps in order to obtain a splendid stable equivalence of Morita type by making use of the gluing met…
We prove a Littlewood-Richardson type formula for $(s_{λ/μ},s_{ν/κ})_{t^k,t}$, the pairing of two skew Schur functions in the MacDonald inner product at $q = t^k$ for positive integers $k$. This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra $C[x]/x^k$ and symmetric groups.
Morita equivalences between cyclotomic KLR algebras in types $\mathtt{C}_\infty$ and $\mathtt{A}_\infty$
通过建立类型C∞一级与A∞二级分圆KLR代数的分级Morita等价，推导出所有类型C∞一级分圆KLR代数的分级分解数和完整子模结构。
Morita theory of finite representations of Leavitt path algebras
本文证明对于无汇点和源点的有限图，Leavitt 路径代数的分级 Grothendieck 群作为保序模同构可推出其局部有限维分级模范畴及有限维模范畴等价，从而为分级分类猜想提供有限表示层面的 Morita 理论支持。
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Injective generation for graded rings
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