Canonical Comultiplication and Double Centraliser Property
نویسندگان
چکیده
In this paper, we show the existence of attached comultiplication structure on $\operatorname{Hom}_{eAe}(eA,D(Ae))$ if an $(eAe,A)$-bimodule $eA$ has double centraliser property over algebra $A$ with idempotent $e$. Then apply it gendo-Gorenstein algebras. As applications, give a sufficient and necessary condition for to be Gorenstein, bocs-theoretic characterisation property.
منابع مشابه
Comultiplication Rules for the Double Schur Functions and Cauchy Identities
The double Schur functions form a distinguished basis of the ring Λ(x ||a) which is a multiparameter generalization of the ring of symmetric functions Λ(x). The canonical comultiplication on Λ(x) is extended to Λ(x ||a) in a natural way so that the double power sums symmetric functions are primitive elements. We calculate the dual Littlewood–Richardson coefficients in two different ways thus pr...
متن کاملThe symplectic ideal and a double centraliser theorem
We interpret a result of Oehms as a statement about the symplectic ideal. We use this result to prove a double centraliser theorem for the symplectic group acting on ⊕s r=0 ⊗ V , where V is the natural module for the symplectic group. This result was obtained in characteristic zero by Weyl. Furthermore, we use this to extend to arbitrary connected reductive groups G with simply connected derive...
متن کاملCanonical Property Designators
The article scrutinises the semantics of canonical property designators of the forms ‘the property of being F’ and ‘F-ness’. First it is argued that, as their form suggests, the former are definite definitions, albeit of a special sort. Secondly, the prima facie plausible classification of the latter as proper names (which is often met in philosophical writings) is rejected. The semantics of su...
متن کاملComultiplication and suspension
We prove the conjecture of Berstein, Hilton, and Ganea that an (n I)-connected CW-complex X with dim X < k(n 2) + 3 which has a co-Ak_,-space structure desuspends. Moreover, we show the following dual of a result of Segal: given a cosimplicial space Y, which is special in the sense that the canonical maps Vz’, Yr + k;, are homotopy equivalences and Yl is 2-connected then there is a functorial d...
متن کاملMultiplication and comultiplication of beliefs
Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coprod...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2023
ISSN: ['1027-5487', '2224-6851']
DOI: https://doi.org/10.11650/tjm/220903