Personal Copy Identical Relations In Lie Algebra

PERSONAL COPY: Identical Relations in Lie Algebra

Identities of Algebras and their Representations

During the past forty years, a new trend in the theory of associative algebras, Lie algebras, and their representations has formed under the influence of mathematical logic and universal algebra, namely, the theory of varieties and identities of associative algebras, Lie algebras, and their representations. The last twenty years have seen the creation of the method of 2-words and $\alpha$-functions, which allowed a number of problems in the theory of groups, rings, Lie algebras, and their representations to be solved in a unified way. The possibilities of this method are far from exhausted. This book sums up the applications of the method of 2-words and $\alpha$-functions in the theory of varieties and gives a systematic exposition of contemporary achievements in the theory of identities of algebras and their representations closely related to this method. The aim is to make these topics accessible to a wider group of mathematicians.

The Personal Development Group

The personal development group is a feature of many counselling and psychotherapy trainings. How does it facilitate personal development? Could it be more effective? Looking from the perspective of the student, this book offers an insight into the workings of the group and the communications that take place within it. The complex relationship between group and individual is explored in the wider context of culture and society. Through examples and exercises, readers can learn about themselves as they learn about the group processes that they are experiencing. Chris Rose charts the course of a PD group through various stages, dealing with fundamental themes such as conflict, authority, resistance and difference. The task is always to keep in focus both the individual experience and the group process. This dual perspective provides group members with important resources to understand and make better use of their own PD group. The elusive task of personal development is vital to the formation of competent counsellors and psychotherapists. Any course that has a PD group will benefit from the understandings that the book can offer, irrespective of theoretical model. This book encourages students to engage with their own development in a pro-active and informed manner. It invites them to challenge attitudes and assumptions in a thoughtful self-reflexive style. This book also provides an introduction to group work that will be valuable for those who are no longer students but are curious about what happens in groups. Whatever the stage of development, there is material to engage and stimulate the reader.