Extensions of finite irreducible modules over rank two Lie conformal algebra
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.
math.RT↗
arXiv subjects
Mengjun Wang
Publications and source records attributed to Mengjun Wang.
RIS-based IMT-2030 Testbed for MmWave Multi-stream Ultra-massive MIMO Communications
As one enabling technique of the future sixth generation (6G) network, ultra-massive multiple-input-multiple-output (MIMO) can support high-speed data transmissions and cell coverage extension. However, it is hard to realize the ultra-massive MIMO via traditional phased arrays due to unacceptable power consumption. To address this issue, reconfigurable intelligent surface-based (RIS-based) antennas are an energy-efficient enabler of the ultra-massive MIMO, since they are free of energy-hungry phase shifters. In this article, we report the performances of the RIS-enabled ultra-massive MIMO via a project called Verification of MmWave Multi-stream Transmissions Enabled by RIS-based Ultra-massive MIMO for 6G (V4M), which was proposed to promote the evolution towards IMT-2030. In the V4M project, we manufacture RIS-based antennas with 1024 one-bit elements working at 26 GHz, based on which an mmWave dual-stream ultra-massive MIMO prototype is implemented for the first time. To approach practical settings, the Tx and Rx of the prototype are implemented by one commercial new radio base station and one off-the-shelf user equipment, respectively. The measured data rate of the dual-stream prototype approaches the theoretical peak rate. Our contributions to the V4M project are also discussed by presenting technological challenges and corresponding solutions.
cs.IT↗
$n$-Lie conformal algebras and its associated infinite-dimensional $n$-Lie algebras
In this paper, we introduce a $\{\lambda_{1\to n-1}\}$-bracket and a distribution notion of an $n$-Lie conformal algebra. For any $n$-Lie conformal algebra $R$, there exists a series of associated infinite-dimensional linearly compact $n$-Lie algebras $\{(\mathscr{L}ie_p\mbox{ }R)_\_\}_{(p\ge1)}$. We show that torsionless finite $n$-Lie conformal algebras $R$ and $S$ are isomorphic if and only if $(\mathscr{L}ie_p\mbox{ }R)_\_\simeq (\mathscr{L}ie_p\mbox{ }S)_\_$ as linearly compact $n$-Lie algebras with $\partial_{t_i}$-action for any $p\ge1$. Moreover, the representation and cohomology theory of $n$-Lie conformal algebras are established. In particular, the complex of $R$ is isomorphic to a subcomplex of $n$-Lie algebra $(\mathscr{L}ie_p\mbox{ }R)_\_$.
math-ph↗
Commutators of pre Lie $n$-algebras and $PL_{\infty}$-algebras
We show that a $PL_{\infty}$-algebra $V$ can be described by a nilpotent coderivation of degree $-1$ on coalgebra $P^*V$. Based on this result, we can generalise the result of T. Lada and show that every $A_{\infty}$-algebra carries a $PL_{\infty}$-algebra structure and every $PL_{\infty}$-algebra carries an $L_{\infty}$-algebra structure. In particular, we obtain a pre Lie $n$-algebra structure on an arbitrary partially associative $n$-algebra and deduce pre Lie $n$-algebras are $n$-Lie admissible.
math.KT↗