Yoneda Ext-algebras of Takeuchi smash products

Acta Mathematica Sinica, English Series, 2006

In this paper, we offer a graded equivalence between the quotient categories defined by any graded Morita-Takeuchi context via certain modifications of the graded cotensor functors. As a consequence, we show a commutative diagram that establish the relation between the closed objects of the categories gr C and M C , where C is a graded coalgebra.

Journal of Algebra, 2012

Nagoya Mathematical Journal, 2021

This is a general study of twisted Calabi–Yau algebras that are $\mathbb {N}$ -graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi–Yau algebras of dimension 0 as separable k-algebras, and we similarly characterize graded twisted Calabi–Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi–Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension.

Journal of Applied Mathematics and Physics

The goal of this paper is to investigate whether the Ext-groups of all pairs

A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A#H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A and a finite-dimensional Hopf algebra H that acts on it; (ii) how the Nakayama automorphism of a graded twist of A is related to the Nakayama automorphism of A; and (iii) that the Nakayama automorphism of a skew Calabi-Yau algebra A has trivial homological determinant in case A is noetherian, connected graded, and Koszul.

In this paper we explore the relations between the Hochschild cohomology of an algebra over some field and the Hochschild cohomology of its smash product with a finite group. Basically we are concentrated on the case where the group under consideration is an extension of a cyclic p-group by some p ′-group, where p is the characteristic of the ground field. * The first named author supported by CNPQ (grant number 300858/2004-3), and also by a tematic project of Fapesp (Project number: 2014/09310-5) † The second named author was supported by a pos-doc scholarship of Fapesp process number 2014/19521-3 1 projective resolution of A#kG using bimodule projective resolutions of A and kG satisfying some properties. The authors of [3] do the same using a bimodule projective resolution of A and a kG-projective resolution of a trivial module. They use this construction to obtain a spectral sequence connecting the Hochschild homology of A and A#kG. In this paper we use a similar construction to explore the Hochschild cohomology. An attempt to obtain some results in the p-modular case was made by the second author in [4]. The results obtained there do not give a good general answer, but they allow to connect the Hochschild cohomology of A and the Hochschild cohomology of A#kC 3 for some specific algebra A over a field of characteristic 3. This work was motivated by the following situation. Let R be an algebra, T R be its trivial extention by DR and R n be an algebraR/ν n ∞ , whereR is a repetetive algebra of R and ν ∞ its Nakayama automorphism. Then it is well known that T R is Morita equivalent to R n #kC n , where C n is generated by a Nakayama automorphism of R n. To see this one can apply the duality theorem of Cohen-Montgomery (see [10]) to the fact that R n is a smash product of T R with the cyclic group C n. Using results of [6] we see that any Nakayama automorphism acts trivially on Hochschild cohomology with coefficients in the regular module and so HH * (R n) is a subalgebra of HH * (T R) if char k ∤ n. So the description of HH * (R n) can be easily obtained from the description of HH * (T R). The examples which we know indicates that almost same fact has to be true in the case char k | n. This motivates us to study this case and obtain a desirable result (see Theorem 14.4). We recall that an algebra B = A/I is called a singular extension of A by I if I 2 = 0. The current work is mainly devoted to the case where G is a trivial extension of a cyclic p-group by some p ′-group, where p = char k. Moreover, the most powerful results were obtained in the case where the spectral sequence mentioned above is (3, 2)-degenerated, i.e. its third page has only two nonzero columns. In the most general terms, our result in this case is as follows. There is a subalgebra A

2004

In this work we study the class of algebras satisfying a duality property with respect to Hochschild homology and cohomology, as in [VdB]. More precisely, we consider the class of algebras A such that there exists an invertible bimodule U and an integer number d with the property H•(A, M) ∼= Hd−•(A, U ⊗A M), for all A-bimodules M . We will show that this class is closed under localization and under smash products with respect to Hopf algebras satisfying also the duality property. We also illustrate the subtlety on dualities with smash products developing in detail the example S(V )#G, the crossed product of the symmetric algebra on a vector space and a finite group acting linearly on V .

Journal of Algebra, 2017

We define the partial group cohomology as the right derived functor of the functor of partial invariants, we relate this cohomology with partial derivations and with the partial augmentation ideal and we show that there exists a Grothendieck spectral sequence relating cohomology of partial smash products with partial group cohomology and algebra cohomology.

Tohoku Mathematical Journal, 1971

IAEME PUBLICATION, 2020

Candlestick Technical analysis also is known as Japanese Candlestick charting oldest for of financial market analysis originated in japan 300 years ago. Last 50 years, this technique attracted considerable importance in the west at the application level. This study tested the predictability of various bullish reversal candlestick patterns in combination with stop loss strategy on 17 stocks of India's leading stock market benchmark index NIFTY 50 for the period of 16 years from 2000 to 2015. Back testing methodology applied to identify the top 10 candlestick patterns based on the frequency of occurrence during the study period. The profitability is analyzed using Sharpe and Sortino ratios on the back tested results for the 10-day holding period returns for the top 4 most occurring candlestick patterns on a stock-specific basis. The results of the study show that Harami and strong-line candlestick patterns are highly profitable.