Supernovae (SNe) are one of the most spectacular astronomical spectacles in the universe.SNe occurs at the end of stellar evolution and can rival the brightness of its host galaxy.Up to now, the study of SNe is an important part of both astrophysics and cosmology. SNe encompass extremely complex physical processes that have a crucial impact on star formation and evolution, and the chemical evolution of galaxies. Type Ia supernovae (SNe Ia) can be used as cosmic distance indicators, cosmic ray accelerators in cosmic heavy element factories and galaxy evolution. Based on SNe Ia distance measurements, it has been discovered that the universe is expanding at an accelerated rate, most possibly driven by dark energy.In this article, we will present in detail the SNe classification and production mechanism, the observational features and current studies of SNe Ia, the progenitor models of SNe Ia, and our work on the AGB donor channel. The main progenitor models for SNe Ia are the single degenerate model and the double degenerate model. In the single degenerate model, a carbon-oxygen white dwarf (CO WD) accretes material from its non-degenerate companion, increasing its mass to the Chandrasekhar mass limit and producing a SN Ia. The non-degenerate companion can be a main-sequence star, sub-giant, red giant, asymptotic giant branch (AGB) star, or helium star.For semidetached WD+AGB star system, we employ an integral mass-transfer method to calculate the mass-transfer process in this channel. We find that semidetached WD+AGB star system can produce SNe Ia through stable mass-transfer process. In addition, we also consider stellar wind accretion process for the detached WD+AGB star systems. We given the initial parameter space of WD+AGB star systems in both cases. The symbiotic star sample AT 2019qyl can be covered by our parameter space, so we suggest that AT 2019qyl could be the potential candidate of SNe Ia with AGB donor.
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