Degree Stable Lie Algebras I

Abstract

We define a degree stable Lie algebra. Since the special type Lie algebra S+(2) is degree stable, we find the automorphism group Aut Lie (S+(2)) of the Lie algebra S+(2) and prove the Jacobian conjecture of the Lie algebra S+(2).

Wireless brain signal acquisition circuits for body sensor network

“…The measured result reveals that developing an ultra low-power EEG acquisition SOC is possible. To transmit the EEG signal through wireless communication, a 2.4 GHz fully integrated RF-transmitter with a merged PA and up- TABLE III SUMMARIZED PERFORMANCES OF THE PROPOSED RF FRONT-END OF THE TRANSMITTER AND ITS COMPARISON WITH PREVIOUSLY PUBLISHED STUDIES 2006 [14] 2007 [15] 2008 [16] 2009 [17] This work Power supply 1. specification. An SHIL-QVCO, with cross-coupled and current reuse topology, has also been proposed to provide the quadrature signals for I/Q modulation/demodulation.…”

Automorphism Group of a Special Type Lie Algebra I

“…For any l in W (n, m, s), we can define the Lie degree deg Lie (l) as the highest degree of non-zero terms of l. The Witt algebra W (0, 0, 1) and the centerless Virasoro algebra W (0, 1, 0) are self-centralizing (see [5]). Furthermore, they are degree-stabilizing (see [10]). The special type Lie algebra…”

“…Assume s 1 = 0, i.e., θ([x∂ 2 , y∂ 1 ]) can be written as (8). First assume that θ(∂ 1 ) can be written as (10) such that it has the maximal term in the (b 1 )-…”

“…Rudakov [11] determined the continuous automorphisms of the topological Cartan type Lie algebras. The automorphism group Aut Lie (S + (2)) of the Lie algebra S + (2) = S(0, 0, 2) is determined in [10]. In this paper, we determine the automorphism group Aut Lie (S(1, 0, 2)) of the Lie algebra S(1, 0, 2) which contains S + (2) = S(0, 0, 2).…”

“…Proof. Thanks to Lemmas 3.1-3.3 in [10], the proof of the theorem is straightforward by Lemmas 3.1-3.3. Thus, it is omitted.…”