short exact sequence
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2021 ◽  
Vol 10 (4) ◽  
pp. 553
Author(s):  
Yudi Mahatma

Inspired by the notions of the U-exact sequence introduced by Davvaz and Parnian-Garamaleky in 1999, and of the chain U-complex introduced by Davvaz and Shabani-Solt in 2002, Mahatma and Muchtadi-Alamsyah in 2017 developed the concept of the U-projective resolution and the U-extension module, which are the generalizations of the concept of the projective resolution and the concept of extension module, respectively. It is already known that every element of a first extension module can be identified as a short exact sequence. To the simple, there is a relation between the first extension module and the short exact sequence. It is proper to expect the relation to be provided in the U-version. In this paper, we aim to construct a one-one correspondence between the first U-extension module and the set consisting of equivalence classes of short U-exact sequence.Keywords: Chain U-complex, U-projective resolution, U-extension module


Author(s):  
Jędrzej Garnek

AbstractLet X be an algebraic curve with a faithful action of a finite group G over a field k. We show that if the Hodge–de Rham short exact sequence of X splits G-equivariantly then the action of G on X is weakly ramified. In particular, this generalizes the result of Köck and Tait for hyperelliptic curves. We discuss also converse statements and tie this problem to lifting coverings of curves to the ring of Witt vectors of length 2.


2021 ◽  
Vol 52 ◽  
Author(s):  
Farshid Saeedi ◽  
Nafiseh Akbarossadat

Let $L$ be an $n$-Lie algebra over a field $\F$. In this paper, we introduce the notion of non-abelian tensor square $L\otimes L$ of $L$ and define the central ideal $L\square L$ of it. Using techniques from group theory and Lie algebras, we show that that $L\square L\cong L^{ab}\square L^{ab}$. Also, we establish the short exact sequence\[0\lra\M(L)\lra\frac{L\otimes L}{L\square L}\lra L^2\lra0\]and apply it to compute an upper bound for the dimension of non-abelian tensor square of $L$.


2020 ◽  
Vol 251 (3) ◽  
pp. 419-426
Author(s):  
I. Panin

Author(s):  
Mingyan Simon Lin

Abstract In this paper, we seek to prove the equality of the $q$-graded fermionic sums conjectured by Hatayama et al. [ 14] in its full generality, by extending the results of Di Francesco and Kedem [ 9] to the non-simply laced case. To this end, we will derive explicit expressions for the quantum $Q$-system relations, which are quantum cluster mutations that correspond to the classical $Q$-system relations, and write the identity of the $q$-graded fermionic sums as a constant term identity. As an application, we will show that these quantum $Q$-system relations are consistent with the short exact sequence of the Feigin–Loktev fusion product of Kirillov–Reshetikhin modules obtained by Chari and Venkatesh [ 5].


2020 ◽  
pp. 1-14
Author(s):  
Youjun Tan ◽  
Senrong Xu

Abstract By using a representation of a Lie algebra on the second Hochschild cohomology group, we construct an obstruction class to extensibility of derivations and a short exact sequence of Wells type for an abelian extension of an associative algebra.


2020 ◽  
Vol 48 (6) ◽  
pp. 2639-2654
Author(s):  
Septimiu Crivei ◽  
Derya Keskin Tütüncü ◽  
Rachid Tribak

2020 ◽  
Vol 10 (08) ◽  
pp. 719-725
Author(s):  
宏涛 范

2019 ◽  
Vol 69 (6) ◽  
pp. 1293-1302
Author(s):  
Morteza Jafari ◽  
Akbar Golchin ◽  
Hossein Mohammadzadeh Saany

Abstract Yuqun Chen and K. P. Shum in [Rees short exact sequence of S-systems, Semigroup Forum 65 (2002), 141–148] introduced Rees short exact sequence of acts and considered conditions under which a Rees short exact sequence of acts is left and right split, respectively. To our knowledge, conditions under which the induced sequences by functors Hom(RLS, –), Hom(–, RLS) and AS ⊗ S– (where R, S are monoids) are exact, are unknown. This article addresses these conditions. Results are different from that of modules.


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