The Cultural Psychological Motivations and Strategies for theDevelopment of Cultural Industry: An Interpretation of Social CulturalPsychology Based on the Engel's Theorem

The cultural industry is an industry that takes culture and creativity as the core of product design, faces the masses, and takes the cultural identity of the masses and the cultural and psychological characteristics of social groups as reference factors for marketing and development. The key to its success lies in its social and cultural psychology. Perception and use. And Engel’s theorem is a typical theory that reflects the economic and cultural level of the country and local people and the psychological state of needs. The analysis of cultural industries based on it can also help contemporary cultural creative workers to more intuitively understand the social market needs and maintain the cultural industry healthy growth.

Nilpotency of the Ordinary Lie-algebra of an n-Lie Algebra

In this paper, we generalize to n-Lie algebras a corollary of the well-known Engel's theorem which offers some justification for the terminology "nilpotent" and we construct a nilpotent ordinary Lie algebra from a nilpotent n-Lie algebra.

ON NILPOTENT LEIBNIZ n-ALGEBRAS

We study the nilpotency of Leibniz n-algebras related with the adapted version of Engel's theorem to Leibniz n-algebras. We also deal with the characterization of finite-dimensional nilpotent complex Leibniz n-algebras.