Fuzzy Lie Algebras Muhammad Akram by Muhammad Akram 9789811332203, 9811332207 instant download after payment.

Lie algebras (also termed as infinitesimal groups) appeared in mathematics at the
end of the nineteenth century through the works of Sophus Lie and Wilhelm Killing
in connection with the study of Lie groups. They also occurred in implicit form
somewhat earlier in mechanics. The term “Lie algebra” itself was introduced by H.
Weyl in 1934. Since the algebra and topology of a Lie group are closely entwined,
Lie algebras which are regarded as tangent spaces at the identity element of the
associated Lie group are used to study the structure of Lie groups. Thus, the
employment of Lie algebra rids of the topological complexity. Hence, the role of
Lie algebras increased in proportion to the place taken by Lie groups in geometry
and also in classical and quantum mechanics. The apparatus of Lie algebras is not
only a powerful tool in the theory of finite groups but also a source of elegant
problems in linear algebra. The notion of Lie superalgebras was introduced by Kac
in 1977 as a generalization of the theory of Lie algebras. In 1985, Filippov introduced
the concept of n-Lie algebras (n
2). The definition when n = 2 agrees with
the usual definition of a Lie algebra.
Fuzzy set theory was proposed in 1965 by Lofti A. Zadeh from the University of
California, Berkeley. Fuzzy set theory has been developed by many scholars in
various directions. Azriel Rosenfeld discussed fuzzy subgroups in 1971, and his
paper led to a new area in fuzzy mathematics. Since then many mathematicians
have been involved in extending the concepts and results of abstract algebra to the
broader framework of the fuzzy setting.
This book introduces readers to fundamental theories such as fuzzy Lie subalgebras,
fuzzy Lie ideals, anti-fuzzy Lie ideals, fuzzy Lie superalgebras, and hesitant
fuzzy Lie ideals over a field. The concepts of nilpotency of intuitionistic fuzzy Lie
ideals, intuitionistic fuzzy Killing form, m-polar fuzzy Lie algebras, ð2;2 _qÞfuzzy
Lie ideals, and rough fuzzy Lie algebras are also presented. Another goal of
this book is to present fuzzy ideals and Pythagorean fuzzy ideals of n-Lie algebras.
Therefore, this book presents a valuable contribution for students and researchers
in fuzzy mathematics, especially for those interested in fuzzy algebraic structures.
The author is a reputed researcher in the fields of fuzzy algebras, fuzzy graphs, and
fuzzy decision-making systems. I believe that he will be appreciated by both the
experts and those who aim to apply the large collection of ideas on classical and
quantum mechanics, quantum field theory, computer vision, and mobile robot
control that he supplies in this book.