اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the Associative Algebra Kernels and Obstruction
92
0
0.0
(
0
)
تأليف
Zelong Li
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The theory of abstract kernels in non-trivial extensions for many kinds of algebraical objects, such as groups, rings and graded rings, associative algebras, Lie algebras, restricted Lie algebras, DG-algebras and DG-Lie algebras, has been widely studied since 1940s. Gerhard Hochschild firstly treats associative algebra as an generic type in the series of kernel problems. He proves the theorem of constructing kernel by presenting many tedious relations that may lost the readers today. In this paper, we shall illustrate the formulation and recast it for Lie algebra(-oid) kernels. We also prove the independence of 3-cocycle in the case of associative algebra. Finally, we use the universal enveloping algebra of Lie algebra to reduce the difficulty of a direct construction for the derivation algebras.
قيم البحث
اقرأ أيضاً
In this paper, we provide a new proof of the stable Adams conjecture. Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the $mathrm{K}$-theory functor to a multi-natural t
ransformation. We also point out that the original proof of the stable Adams conjecture is incorrect and present a correction. This correction is crucial to our main application. We settle the question on the height of higher associative structures on the mod $p^k$ Moore spectrum $mathrm{M}_p(k)$ at odd primes. More precisely, for any odd prime $p$, we show that $mathrm{M}_p(k)$ admits a Thomified $mathbb{A}_n$-structure if and only if $n < p^k$. We also prove a weaker result for $p=2$.
This paper continues the study of the lower central series quotients of an associative algebra A, regarded as a Lie algebra, which was started in math/0610410 by Feigin and Shoikhet. Namely, it provides a basis for the second quotient in the case whe
n A is the free algebra in n generators (note that the Hilbert series of this quotient was determined earlier in math/0610410). Further, it uses this basis to determine the structure of the second quotient in the case when A is the free algebra modulo the relations saying that the generators have given nilpotency orders. Finally, it determines the structure of the third and fourth quotient in the case of 2 generators, confirming an answer conjectured in math/0610410. Finally, in the appendix, the results of math/0610410 are generalized to the case when A is an arbitrary associative algebra (under certain conditions on $A$).
We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of truncated min
imal A-infinity algebra structures. We also consider the Bousfield-Kan spectral sequence for the moduli space of A-infinity algebras. We compute up to the second page, terms and differentials, of these spectral sequences in terms of Hochschild cohomology.
From the symmetry between definitions of left and right divisors in associative $D$-algebra $A$, the possibility to define quotient as $Aotimes A$-number follows. In the paper, I considered division and division with remainder. I considered also definition of prime $A$-number.
We compute the $C_p$-equivariant dual Steenrod algebras associated to the constant Mackey functors $underline{mathbb{F}}_p$ and $underline{mathbb{Z}}_{(p)}$, as $underline{mathbb{Z}}_{(p)}$-modules. The $C_p$-spectrum $underline{mathbb{F}}_p otimes u
nderline{mathbb{F}}_p$ is not a direct sum of $RO(C_p)$-graded suspensions of $underline{mathbb{F}}_p$ when $p$ is odd, in contrast with the classical and $C_2$-equivariant dual Steenrod algebras.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
