اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCorrection to: HZ-algebra spectra are differential graded algebras
152
0
0.0
(
0
)
تأليف
Brooke Shipley
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This correction article is actually unnecessary. The proof of Theorem 1.2, concerning commutative HQ-algebra spectra and commutative differential graded algebras, in the authors paper [American Journal of Mathematics vol. 129 (2007) 351-379 (arxiv:math/0209215v4)] is correct as originally stated. Neil Strickland carefully proved that D is symmetric monoidal; so Proposition 4.7 and hence also Theorem 1.2 hold as stated. Stricklands proof will appear in joint work with Stefan Schwede; see related work in Stricklands [arxiv:0810.1747]. Note here D is defined as a colimit of chain complexes; in contrast, non-symmetric monoidal functors analogous to D are defined as homotopy colimits of spaces in previous work of the author.
قيم البحث
اقرأ أيضاً
Let $H$ be a finite dimensional semisimple Hopf algebra, $A$ a differential graded (dg for short) $H$-module algebra. Then the smash product algebra $A#H$ is a dg algebra. For any dg $A#H$-module $M$, there is a quasi-isomorphism of dg algebras: $mat
hrm{RHom}_A(M,M)#Hlongrightarrow mathrm{RHom}_{A#H}(Mot H,Mot H)$. This result is applied to $d$-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras
The paper gives a new proof that the model categories of stable modules for the rings Z/(p^2) and (Z/p)[epsilon]/(epsilon^2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two d
ifferential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with non-isomorphic K-theories.
We show that the homotopy category of commutative algebra spectra over the Eilenberg-Mac Lane spectrum of the integers is equivalent to the homotopy category of E-infinity-monoids in unbounded chain complexes. We do this by establishing a chain of Qu
illen equivalences between the corresponding model categories. We also provide a Quillen equivalence to commutative monoids in the category of functors from the category of finite sets and injections to unbounded chain complexes.
Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of homological commutative algebra.
The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When the Koszul
DG algebra $A$ is AS-regular, the Ext-algebra $E$ of $A$ is Frobenius. In this case, similar to the classical BGG correspondence, there is an equivalence between the stable category of finitely generated left $E$-modules, and the quotient triangulated category of the full triangulated subcategory of the derived category of right DG $A$-modules consisting of all compact DG modules modulo the full triangulated subcategory consisting of all the right DG modules with finite dimensional cohomology. The classical BGG correspondence can derived from the DG version.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
