In the paper we find a basis of identities for the variety generated by semigroups of relations with an operation of reflexive double cylindrification.

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This article provides examples of the choreographer's work with the composer and artist in creating a choreographic work, how they combine their professional knowledge, complement each other, help in creative work, and emphasize small mistakes, which improve joint creative work. The question of how a composer helps a choreographer to create and change certain dance movements in relation to music, so that they would be harmoniously combined with a musical score in creative work, is analyzed. Algorithms of work of a choreographer, composer and artist during the staging of a ballet or dance number are studied, in which it is described in detail what work each of them should perform at a certain stage of creating a performance. The work of a choreographer who creates the dance basis of a performance, whose task is to build a dance or the whole performance in such a way as to maintain and increase the audience's interest, is analyzed, and an important component such as success in a profession that depends on education , a talent that is honed all his life. Talented performers are not always good choreographers. It also describes the work of the composer, who musically gives the mood and character of movements, as well as emphasizes every pose and pause in the dance, whose task is to feel the choreographer's idea and create music that would fully reflect the opinion of the choreographer and help him bring choreography to life. the work of a composer who creates a musical score of ballet, given its theatrical affiliation, due to the stage action and genre nature of the performance. The material of the artist's works is also provided, thanks to which the created choreographic work acquires amazing colors not only in costumes and props, but also powerful design with stage decorations and light, thanks to which the joint work acquires a complete look. artist increases significantly than in solving problems related to the design of a concert number, concert program, but this does not mean that in the latter case, the creative task is easier.