Green Communications: Techniques and Challenges

Green innovation has drawn a gigantic measure of consideration with the improvement of the advanced world. Correspondingly with the advancement in correspondence innovation the ventures and analysts are centering to make this correspondence as green as would be prudent. In cell innovation the advancement of 5G is the subsequent stage to satisfy the client requests and it will be accessible to the clients in 2020. This will build the vitality utilization by which will result in overabundance emanation of co2. In this paper distinctive methods for the green correspondence innovation and a few difficulties are talked about. These methods incorporate gadget to-gadget correspondence (D2D), huge Multiple-Input Multiple-Output (MIMO) frameworks, heterogeneous systems and Green Internet of Things (IoT).

Analogs of the Green and Puig correspondences for twisted group algebras

In the modular representation theory of finite groups, we show that the standard derivation of the Green correspondence lifts to a derivation of a Green correspondence for twisted group algebras (Theorem 1.3). Then, from these results we derive a lift of the Puig correspondences for twisted group algebras (Theorem 1.6).Clearly twisted group algebras arise naturally in finite group modular representation theory. We conclude with some suggestions for applications in this mathematical area.

A block extension of categorical results in the Green correspondence context

In [J. Pure Appl. Algebra 2 (1972), 371–393, Theorem 4.1], J. A. Green shows that the Green Correspondence in Finite Group Modular Representation Theory is a consequence of an equivalence between two quotient categories of appropriate subcategories in the Green Correspondence context. In [Adv. Math. 104 (1994), 297–314, Theorems 3.5, 3.6 and 3.7], M. Auslander and M. Kleiner prove a similar result. M. Linckelmann suggested that the quotient categories in these results are the same. Utilizing extensions of [The Representation Theory of Finite Groups, North-Holland, Amsterdam, 1982, III, Theorem 7.8] or [Representations of Finite Groups, Academic Press, San Diego, 1988, Chapter 5, Corollary 3.11], we extend these results to blocks of finite groups. In order to state and prove our results and to remain relatively self-contained, we follow the procedures of [Adv. Math. 104 (1994), 297–314] in the Green Correspondent context. This is presented in Section 1. In Section 2 we present our main results. In Section 3 we give a very short proof of a theorem of H. Fitting for 𝒪-algebras that is essential in the proof of basic results of J. A. Green, [J. Pure Appl. Algebra 2 (1972), 371–393, Lemma 3.9 and Theorem 3.10].