منابع مشابه
Stratifications and Mackey Functors Ii: Globally Defined Mackey Functors
We describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero they form a highest weight category and we also determine precisely when this category is semisimple. This approach is used to show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite pa...
متن کاملDecomposable Functors and the Exponential Principle, Ii
We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural transformations (composition operators), and we show that, somewhat surprisingly, a single axiom for the composition already suffices to guarantee validity of...
متن کاملSymmetries of a Generic Coaction
If B is C∗-algebra of dimension 4 ≤ n < ∞ then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say Gaut(B̂), have the same fusion rules as the ones of SO(3). As consequences, we get (1) a structure result for Gaut(B̂) in the case where B is a matrix algebra (2) if n ≥ 5 then the dual Ĝaut(B̂) is not amenable (3) if n ≥ 4 then the fixed point subfa...
متن کاملSpectral Mackey Functors and Equivariant Algebraic K - Theory ( Ii )
We study the “higher algebra” of spectral Mackey functors, which the first named author introduced in Part I of this paper. In particular, armed with our new theory of symmetric promonoidal ∞-categories and a suitable generalization of the second named author’s Day convolution, we endow the∞-category of Mackey functors with a wellbehaved symmetric monoidal structure. This makes it possible to s...
متن کاملThe Planar Algebra of a Coaction
We study actions of “compact quantum groups” on “finite quantum spaces”. According to Woronowicz and to general C-algebra philosophy these correspond to certain coactions v : A → A ⊗ H . Here A is a finite dimensional C-algebra, and H is a certain special type of Hopf ∗-algebra. If v preserves a positive linear form φ : A → C, a version of Jones’ “basic construction” applies. This produces a ce...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2018
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2018.293.301